Problem

The probability that a student has a Visa card (event $\mathcal{H}$ is .60. The probability that a student has a MasterCard (event $M$ is .20. The probability that a student has both cards is .12 . (a) Find the probability that a student has either a Visa card or a MasterCard. (Round your answer to 2 decimal places.) Probability (b) In this problem, are $V$ and $M$ independent?

Solution

Step 1 :Given that the probability that a student has a Visa card (event $\mathcal{H}$) is 0.60, the probability that a student has a MasterCard (event $M$) is 0.20, and the probability that a student has both cards is 0.12.

Step 2 :We can find the probability that a student has either a Visa card or a MasterCard using the formula for the probability of the union of two events: $P(A \cup B) = P(A) + P(B) - P(A \cap B)$.

Step 3 :Substituting the given probabilities into the formula, we get $P(V \cup M) = P(V) + P(M) - P(V \cap M) = 0.60 + 0.20 - 0.12 = 0.68$.

Step 4 :Therefore, the probability that a student has either a Visa card or a MasterCard is \(\boxed{0.68}\).

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Source: https://solvelyapp.com/problems/RVjSYESr7z/

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