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
[tex] P(A|B) = \frac{P(A \cap B)}{P(A)} [/tex]
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
[tex] P(P|R) = \frac{P(P \cap R)}{P(R)} = \frac{0.15}{50} = 0.30 [/tex]
2. conditional probability that a bag of red candy also contains pink candy is
[tex] P(R|P) = \frac{P(R \cap P)}{P(P)} = \frac{0.15}{0.25} = 0.60 [/tex]
From this, we see that the conditional probability that a bag of red candy also contains pink candy is greater.
