Question

15 cards are selected out of a 52 card deck such that after each card is selected, it is placed back into the deck and the deck is reshuffled. Then the total number of hearts selected follows a binomial distribution.

a) true
b) false

Answer 1

a) true

Explanation:

There are 13 heart-suit cards in a 52 card deck.

Since cards are returned to the deck after each pick, all of the 15 events are independent and have the same likelihood of occurring. Therefore, this experiment follows a binomial distribution with the following properties:

Number of events (n) = 15

Probability of success (Picking a heart) = 13/52 = 1/4

Probability of failure (Not picking a heart) = 39/52 = 3/4

In conclusion, the statement provided is true.