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

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



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



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



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

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