a In draw poker there is about a 49 chance that a randomly d

a. In draw poker there is about a 49% chance that a randomly dealt five-card hand will contain at least two cards of the same denomination. This conclusion is perhaps most readily demonstrated by showing that the probability that the hand does not contain two cards of the same denomination is given by the expression

Justify this expression, and complete the indicated demonstration.

b. In a class of 50 randomly selected students, what is the probability that at least one pair of students will share a birthday?

Hint: This surprisingly large probability is easily obtained by adapting the development in part (a) to calculate the probability that no two students share a birthday

Solution

For a)

If you complete the given, the answer .507.

This can be rounded to 0.51. The probability that you will NOT be dealt 2 cards of the same denomination is p=0.51

Then we can say, the probability that we will be dealt 2 cards of the same denomination is = 1-p

p=0.51

1-0.51= 0.49

Proves 49% chance