An urn contains two red R balls numbered 1 and 2, five white W balls numbered 3, 4, 5, 6 and 7, and three black B balls numbered 8, 9 and 10. A ball is drawn from the urn. What is the probability that it is red or odd-numbered O?
A) Pr(R or
O) =
B) Pr(R or
O) =
C) Pr(R or
O) =
D) Pr(R or
O) =
E) Pr(R or
O) =

Question

An urn contains two red R balls numbered 1 and 2, five white W balls numbered 3, 4, 5, 6 and 7, and three black B balls numbered 8, 9 and 10. A ball is drawn from the urn. What is the probability that it is red or odd-numbered O? ​
A) Pr(R or 
O) = 
B) Pr(R or 
O) = 
C) Pr(R or 
O) = 
D) Pr(R or 
O) = 
E) Pr(R or 
O) =

Quizplus · Accepted Answer

There are three red balls and five odd-numbered balls (3, 5, and 7) that are not red. The probability of drawing a red or odd-numbered ball is the sum of the probabilities of drawing a red ball and an odd-numbered ball minus the probability of drawing both a red and odd-numbered ball (since we would be counting this twice). 
Pr(R or O) = Pr(R) + Pr(O) - Pr(R and O)

Pr(R) = 2/10 (since there are 2 red balls and 10 total balls) 
Pr(O) = 5/10 (since there are 5 odd-numbered balls and 10 total balls) 
Pr(R and O) = 1/10 (since there is only one ball that is both red and odd-numbered, which is ball 3)

Plugging in these values: 
Pr(R or O) = 2/10 + 5/10 - 1/10 = 6/10 = 3/5

Therefore, the probability of drawing a red or odd-numbered ball is 3/5. The answer choice that matches this calculation is C.

An Urn Contains Two Red R Balls Numbered 1 and 2