Question

"The probability that a student has a Visa card (event V) is .73. The probability that a student has a MasterCard (event M) is .18. The probability that a student has both cards is .03.

(a) Find the probabi lity that a student has either a Visa card or a MasterCard. (Round your answer to 2 decimal places.)"
(b) In this problem, are V and M independent?Explain.

Answer 1

(a)0.88

(b)Not Independent

Explanation:

The probability that a student has a Visa card, P(V)= 0.73.

The probability that a student has a MasterCard, P(M)= 0.18.

The probability that a student has both cards, P(M∩V)=0.03

(a)We want to find the probability that a student has either a Visa card or a MasterCard, P(M∪V).

From Probability Theorem,

P(M∪V)=P(M)+P(V)-P(M∩V)

=0.18+0.73-0.03

=0.88

The Probability that a student has MasterCard or Visa card is 0.88.

(b)P(M only)=P(M)-P(M∩V)

=0.18-0.03

=0.15

P(V only)=P(V)-P(M∩V)

=0.73-0.03

=0.70

The two Events are independent if:

P(M)P(V)=P(M∩V)

0.15*0.70=0.105≠0.03

Since the equality does not hold, events M and V are not independent.