Question

Twelve people each have a standard deck of cards. Each person shuffles the deck and draws two cards (without replacement). Anyone who draws at least one diamond wins a prize. To the nearest whole number, about how many of the twelve will win a prize

Answer 1

Answer:

The number of people, of the twelve, who will win a prize is 5.

Step-by-step explanation:

In a standard deck of cards there are 52 cards.

The 52 cards are divided into 4 suits: Hearts, Diamonds, Spades and Clubs, each of 13 cards.

Each of the 12 people draws 2 cards from their standard deck of cards.

Compute the probability of selecting at least 1 diamond as follows:

P (At least 1 diamond) = 1 - P (No diamond)

                                    $=1-\frac{{39\choose 2}}{{52\choose 2}} \\=1-\frac{741}{1326}\\ =1-0.5588\\=0.4412$

The probability of selecting at least 1 diamond is 0.4412.

If a person draws at least 1 diamond he wins a prize.

The expected number of people who will win the prize is:

E (Wins a prize) = n × P (At least 1 diamond)

                          $=12\times0.4412\\=5.2944\\\approx5$

Thus, the number of people of the twelve who will win a prize is 5.