Find the probability
-Elise has put 5 cans (all of the same size) on her kitchen counter; 2 cans of vegetables, 2 cans of Soup , and 1 can of peaches. Her son, Ryan, takes the labels off the cans and throws them away. Elise then chooses 2 cans (without replacement) at random to open. Find the probability that she Will open at least 1 can of soup.
A) $\frac { 3 } { 5 }$
B) $\frac { 9 } { 10 }$
C) $\frac { 7 } { 10 }$
D) $\frac { 4 } { 5 }$

Question

Find the probability
-Elise has put 5 cans (all of the same size) on her kitchen counter; 2 cans of vegetables, 2 cans of Soup , and 1 can of peaches. Her son, Ryan, takes the labels off the cans and throws them away. Elise then chooses 2 cans (without replacement) at random to open. Find the probability that she Will open at least 1 can of soup. 
A) $\frac { 3 } { 5 }$
B) $\frac { 9 } { 10 }$
C) $\frac { 7 } { 10 }$
D) $\frac { 4 } { 5 }$

Quizplus · Accepted Answer

The probability of opening at least 1 can of soup is easier to calculate by finding the probability of the complementary event (not opening any soup cans) and subtracting it from 1. The probability of not picking a soup can in the first pick is $\frac{3}{5}$ (3 non-soup cans out of 5 total cans), and if the first can is not soup, the probability of also not picking a soup can as the second pick is $\frac{2}{4}$ (2 non-soup cans out of the remaining 4 cans). So, the probability of not picking any soup cans is $\frac{3}{5} \times \frac{2}{4} = \frac{6}{20} = \frac{3}{10}$. Therefore, the probability of picking at least one can of soup is $1 - \frac{3}{10} = \frac{7}{10}$.

Find the Probability -Elise Has Put 5 Cans (All of the Same 35\frac { 3 } { 5 }53​

Find the Probability
-Elise Has Put 5 Cans (All of the Same $\frac { 3 } { 5 }$