Question

With a standard deck of cards with 4 suites and 13 ranks:

A: what is the probability that a randomly drawn card is an ace or a heart?

B: Are the events Ace and Heart independent? What about the ace of hearts? Show the calculation to explain why or why not

Answer 1

(A)

P(Ace) = 4/52 = 0.0769

P(Heart) = 13/52 = 0.25

P(Ace & Heart) = 1/52 = 0.0192

So,

By Addition Theorem:
P(Ace OR Heart) = P(Ace) + P(Heart) - P(Ace & Heart)

                        = 0.0769 + 0.25 - 0.0192 = 0.3077

So,

Answer is:

0.3077

(B)

P(Ace) = 0.0769

P(Heart) = 0.25

P(Ace & Heart)= 0.0192

P(Ace) X P(Heart) = 0.0769 X 0.25 = 0.0192

Since P(Ace & Heart) = P(Ace) X P(Heart), the events Ace and Heart are independent.