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A standard deck of playing cards has four suits in two colors: diamonds and hearts are red; clubs and spades are black. Each suit has 13 cards: an ace, the numbers two through ten, a jack, a queen, and a king.

If you drew a card from the deck and then put it back, and repeated this 100 times, about how many times would you expect to draw a card that is a five from any suit?

Answer with a whole number only.

May 3, 2023

#1
+1

Since there are four suits in a deck of cards and each suit has one five, there are a total of four fives in a deck of 52 cards. This means that the probability of drawing a five on any given draw is 4/52, or 1/13.

Since each draw is independent of the others, the probability of drawing a five on each of the 100 draws is also 1/13. Therefore, we can use the formula for the expected value of a binomial distribution to find the expected number of fives in 100 draws:

E(X) = n * p

where E(X) is the expected number of fives, n is the number of trials (100 in this case), and p is the probability of success on each trial (1/13).

Plugging in the values, we get:

E(X) = 100 * (1/13) = 7.69 =~8

So we would expect to draw a five about 7 or 8 times in 100 draws. Note that this is just an expected value and the actual number of fives drawn may vary from this value.

May 3, 2023
edited by Guest  May 3, 2023