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

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

Answer 2

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) = (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) = (P(P \cap R))/(P(R)) = (0.15)/(50) = 0.30`

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


`P(R|P) = (P(R \cap P))/(P(P)) = (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.