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.
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.