A dealer in the Sands Casino in Las Vegas selects 40 cards froma standard deck o

Question

A dealer in the Sands Casino in Las Vegas selects 40 cards froma standard deck of 52 cards. Let Y be the number of red cards(hearts or diamonds) in the 40 cards selected. Which of thefollowing best describes this setting:

(a) Y has a binomial distribution with n = 40observations and probability of success p = 0.5.

(b) Y has a binomial distribution with n=40observations and probability of success p = 0.5, providedthe deck is shuffled well.

(c) Y has a binomial distribution with n=40observations and probability of success p = 0.5, providedafter selecting a card it is replaced in the deck and the deck isshuffled well before the next card is selected.

(d) Y has a normal distribution with mean p = 0.5.

Explanation / Answer

The answer is C: Y has a binomial distribution with n=40 observationsand probability of success p = 0.5, provided afterselecting a card it is replaced in the deck and the deck isshuffled well before the next card is selected. We need to place the card back to the deck because binomialdistribution requires independent trials. we need to place thecards back to remain to have p=0.5 for the next trials

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