Given that P(Visa Card)=0.5 P(Master Card)=0.4 P(Visa Card Master card)=0.25 Part A: P(Only Visa card )=P(Visa)-P(Visan Master) =0.5-0.25 =0.25 P(Only Master Card)=p(Master)-p(visan Master) =0.4-0.25 = 0.15 P(Either Visa OrMASTER) = P(Visa) + P(MASTER) =0.25+0.15 =0.40 Part B: We need to find the probability that an individual has a Visa card given that they have a MasterCard. Using Bayes' theorem, we can write: P(V | M) = P(M | V) * P(V) / P(M) Explanation: where P(M | V) is the probability that an individual has a MasterCard given that they have a Visa card. We can find this probability using the formula for conditional probability: P(M | V) = P(V and M) / P(V) Plugging in the given values, we get: P(MV) 0.25 0.50 = 0.5 Now, we need to find P(M), which is the probability that an individual has a MasterCard. This can be calculated as: P(M) = P(V and M) + P(M only) We have already calculated P(V and M) in part (a) as 0.25. To find P(M only), we can subtract the probability that an individual has both cards from the probability that the individual has a MasterCard, as follows: P(M only) = P(M) - P(V and M) = 0.40 0.25 0.15 Therefore, we have: P(M) = 0.25 +0.15 = 0.40 Now, we can plug in the values into Bayes' theorem to find P(V | M): P(V | M) = P(M | V) * P(V) / P(M) = 0.5 * 0.50 / 0.40 = 0.625 Therefore, the probability that an individual has a Visa card given that they have a MasterCard is 0.625. 1. (10 points) The probability that a selected individual has a Visa card is 0.6. The proba- bility that a selected individual has a Master card is 0.7. The probability that a selected individual has both a Visa card and a Master card is 0.5. (a) (5 points) What is the probability that a selected individual has either a Visa card or a Master card? (b) (5 points) What is the probability that a selected individual has a Visa card given that they have a Master card?