Question

In a random survey of Valentine’s Day candy bags, 50% of bags contained red candy, 25% of bags contained pink candy, and 15% contained both red and pink candy. Explain which is greater: -The conditional probability that a bag with pink candy also contains red candy -The conditional probability that a bag with red candy also contains pink candy

Answer 1

Conditional probability is the probability that an event is occurring while another has occured. Mathematically, we can compute for the conditional probability, P(A|B) as

$P(A|B) = \frac{P(A \cap B)}{P(A)}$

where P(A∩B) is the probability that events A AND B are occurring at the same time and P(A) is the probability for A to happen.

For our case, given that 50% of the bags contain red, 25% contain pink, and 15% contains red & pink. Thus, we have

P(R) = 0.50
P(P) = 0.25
P(R∩P) = 0.15

So, the conditional probability of the events below to happen can be calculated as shown.

1. conditional probability that a bag of pink candy also contains red candy is

$P(P|R) = \frac{P(P \cap R)}{P(R)} = \frac{0.15}{50} = 0.30$

2. conditional probability that a bag of red candy also contains pink candy is

$P(R|P) = \frac{P(R \cap P)}{P(P)} = \frac{0.15}{0.25} = 0.60$

From this, we see that the conditional probability that a bag of red candy also contains pink candy is greater.

Answer 2

Please look at the file below. This should help you.