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