Question 1

Decide whether or not the events are mutually exclusive.
-Being a male and being a nurse

Accepted Answer

Being a male and being a nurse are not mutually exclusive events because a person can be both a male and a nurse at the same time.

Question 2

Decide whether or not the events are mutually exclusive.
-Events A and B defined as follows A card is drawn at random from a deck of cards. Event A is that the card obtained is a face card
And B is the event that the card obtained is a two.

Accepted Answer

Events A and B are mutually exclusive because a card cannot be both a face card and a two at the same time.

Question 3

Find the probability.
-A fair die is rolled. What is the probability of rolling a 3 or a 6?

Accepted Answer

The probability of rolling a 3 or a 6 on a fair six-sided die is $\frac{2}{6}$ because there are two favorable outcomes (rolling a 3 or a 6) out of six possible outcomes. Simplifying $\frac{2}{6}$ gives $\frac{1}{3}$.

Question 4

Decide whether or not the events are mutually exclusive.
-Wearing a coat and wearing a sweater

Accepted Answer

Wearing a coat and wearing a sweater are not mutually exclusive events because one can wear a sweater and then put on a coat over it, meaning both events can occur at the same time.

Question 5

Decide whether or not the events are mutually exclusive.
-Events A and B defined as follows Event A is that at least three of Toni's five cousins are female.
Event B is that at most four of Toni's five cousins are male.

Accepted Answer

Events A and B are not mutually exclusive because it is possible for both events to occur simultaneously. For example, if Toni has three female cousins and two male cousins, both Event A (at least three cousins are female) and Event B (at most four cousins are male) would occur.

Question 6

Find the probability.
-A card is drawn at random from a well-shuffled deck of 52 cards. What is the probability of drawing a face card or a 5?

Accepted Answer

There are 12 face cards (Jacks, Queens, Kings of each suit) and 4 fives in a deck, but since the 5 of hearts, diamonds, clubs, and spades are counted separately, we don't double count them. Thus, we have 12 + 4 = 16 favorable outcomes out of 52. Simplifying 16/52 gives 4/13.

Question 7

Find the indicated probability.
-The age distribution of students at a community college is given below. $$\begin{array} { l r } 
\text { Age (years) } & \text { Number of students (f) } \
\hline \text { Under 21 } & 400 \
21 - 25 & 403 \
26 - 30 & 219 \
31 - 35 & 56 \
\text { Over 35 } & 29 \
\hline & 1107
\end{array}$$ A student from the community college is selected at random. Find the probability that the student is between 26 and 35 inclusive. Round approximations to three decimal places.

Accepted Answer

To find the probability that a randomly selected student is between 26 and 35 years old, inclusive, we add the number of students in the age groups 26 - 30 and 31 - 35, then divide by the total number of students. The calculation is $\frac{219 + 56}{1107} = \frac{275}{1107} \approx 0.248$.

Question 8

Decide whether or not the events are mutually exclusive.
-Being over 30 and being in college

Accepted Answer

Being over 30 and being in college are not mutually exclusive events because a person can be both over 30 years old and be in college at the same time.

Question 9

Find the probability.
-When two balanced dice are rolled, there are 36 possible outcomes. What is the probability that the sum of the numbers on the dice is 6 or 9?

Accepted Answer

The sum is 6 in 5 ways (1,5), (2,4), (3,3), (4,2), (5,1) and 9 in 4 ways (3,6), (4,5), (5,4), (6,3). So, 9 outcomes out of 36 are favorable, giving a probability of $\frac{9}{36} = \frac{1}{4}$.

Question 10

Find the probability.
-A spinner has regions numbered 1 through 21. What is the probability that the spinner will stop on an even number or a multiple of 3?

Accepted Answer

The even numbers between 1 and 21 are 2, 4, 6, 8, 10, 12, 14, 16, 18, 20 (10 in total). The multiples of 3 are 3, 6, 9, 12, 15, 18, 21 (7 in total). However, 6, 12, and 18 are counted twice since they are both even and multiples of 3. Therefore, there are 10 + 7 - 3 = 14 unique numbers that are either even or multiples of 3 out of 21. Thus, the probability is 14/21, which simplifies to 2/3.

Question 11

Find the probability.
-A card is drawn at random from a well-shuffled deck of 52 cards. What is the probability of drawing a face card or a red card?

Accepted Answer

The answer of Find the probability.
-A card is drawn at...

Question 12

Decide whether or not the events are mutually exclusive.
-Events A and B defined as follows A card is drawn at random from a deck of cards. Event A is that the card obtained is a face card
And B is the event that the card obtained is a spade.

Accepted Answer

Events A and B are not mutually exclusive because a card can be both a face card and a spade (e.g., the Jack, Queen, or King of Spades).

Question 13

Find the probability.
-When two balanced dice are rolled, there are 36 possible outcomes. Find the probability that the sum is a multiple of 3 or greater than 4.

Accepted Answer

The sums that are multiples of 3 are 3, 6, 9, and 12. The sums greater than 4 are 5 through 12. Combining these, we cover all sums from 3 to 12 except for 4. There are 3 ways to get a sum of 4 (1+3, 2+2, 3+1) out of 36 possible outcomes, so the probability of getting a sum that is either a multiple of 3 or greater than 4 is 1 - (3/36) = 33/36 = 11/12. However, this calculation overlooks the fact that the sums of 5 and 7 are counted twice, once as being greater than 4 and once as being multiples of 3. Correctly accounting for all unique outcomes that meet the criteria without double-counting, we find that the actual number of favorable outcomes is more extensive, leading to the correct probability being higher, which is $\frac{8}{9}$.

Question 14

Find the probability.
-When two balanced dice are rolled, there are 36 possible outcomes. Find the probability that either doubles are rolled or the sum of the dice is 8.

Accepted Answer

The answer of Find the probability.
-When two balanced dice are...

Question 15

Find the probability.
-A lottery game has balls numbered 0 through 9. If a ball is selected at random, what is the probability of selecting an even numbered ball or a 3?

Accepted Answer

The even numbers are 0, 2, 4, 6, and 8, which makes 5 even numbers. Including the number 3, there are 6 favorable outcomes out of 10 possible outcomes, giving a probability of $\frac{6}{10}$ or $\frac{3}{5}$.

Question 16

Find the probability.
-A card is drawn at random from a well-shuffled deck of 52 cards. What is the probability of drawing a face card or a spade?

Accepted Answer

The answer of Find the probability.
-A card is drawn at...

Question 17

Decide whether or not the events are mutually exclusive.
-Having good reading skills and having good math skills

Accepted Answer

Having good reading skills and having good math skills are not mutually exclusive because it is possible for someone to possess both skills simultaneously.

Question 18

Decide whether or not the events are mutually exclusive.
-Being a teenager and being a United States Senator

Accepted Answer

The answer of Decide whether or not the events are...

Question 19

Find the probability.
-A fair die is rolled. What is the probability of rolling an odd number or a number less than 3?

Accepted Answer

The answer of Find the probability.
-A fair die is rolled....

Question 20

Decide whether or not the events are mutually exclusive.
-Events A and B defined as follows Event A is that at least three of Toni's five cousins are female.
Event B is that at least three of Toni's five cousins are male.

Accepted Answer

Events A and B are mutually exclusive because they cannot both happen at the same time. If at least three of Toni's five cousins are female, then at least three of them cannot be male.

Quiz 11: Probability

Decide whether or not the events are mutually exclusive. -Being a male and being a nurse

Decide whether or not the events are mutually exclusive. -Events A and B defined as follows A card is drawn at random from a deck of cards. Event A is that the card obtained is a face card And B is the event that the card obtained is a two.

Find the probability. -A fair die is rolled. What is the probability of rolling a 3 or a 6?

Decide whether or not the events are mutually exclusive. -Wearing a coat and wearing a sweater

Decide whether or not the events are mutually exclusive. -Events A and B defined as follows Event A is that at least three of Toni's five cousins are female. Event B is that at most four of Toni's five cousins are male.

Find the probability. -A card is drawn at random from a well-shuffled deck of 52 cards. What is the probability of drawing a face card or a 5?

Decide whether or not the events are mutually exclusive. -Being over 30 and being in college

Find the probability. -When two balanced dice are rolled, there are 36 possible outcomes. What is the probability that the sum of the numbers on the dice is 6 or 9?

Find the probability. -A spinner has regions numbered 1 through 21. What is the probability that the spinner will stop on an even number or a multiple of 3?

Find the probability. -A card is drawn at random from a well-shuffled deck of 52 cards. What is the probability of drawing a face card or a red card?

Decide whether or not the events are mutually exclusive. -Events A and B defined as follows A card is drawn at random from a deck of cards. Event A is that the card obtained is a face card And B is the event that the card obtained is a spade.

Find the probability. -When two balanced dice are rolled, there are 36 possible outcomes. Find the probability that the sum is a multiple of 3 or greater than 4.

Find the probability. -When two balanced dice are rolled, there are 36 possible outcomes. Find the probability that either doubles are rolled or the sum of the dice is 8.

Find the probability. -A lottery game has balls numbered 0 through 9. If a ball is selected at random, what is the probability of selecting an even numbered ball or a 3?

Find the probability. -A card is drawn at random from a well-shuffled deck of 52 cards. What is the probability of drawing a face card or a spade?

Decide whether or not the events are mutually exclusive. -Having good reading skills and having good math skills

Decide whether or not the events are mutually exclusive. -Being a teenager and being a United States Senator

Find the probability. -A fair die is rolled. What is the probability of rolling an odd number or a number less than 3?

Decide whether or not the events are mutually exclusive. -Events A and B defined as follows Event A is that at least three of Toni's five cousins are female. Event B is that at least three of Toni's five cousins are male.