Question

Construct the probability distribution for the value of a 2-card hand dealt from a standard deck of 52 cards (all face cards have a value of 10 and an ace has a value of 11). a) What is the probability of being dealt a hand that adds up to 21? b) What is the probability of being dealt a hand that adds up to 20? Construct a chart for the cumulative probability distribution. c) What is the probability of being dealt a 16 or less? d) What is the probability of being dealt between 12 and 16 (inclusive)? e) What is the probability of being dealt between 17 and 20 (inclusive)? f) Find the expected value of a two card hand

Answer 1

a. There are 4 aces and twelve face cards and 4 10s in a deck of 52 cards.

4/52(for aces)*16/51(for cards = 10 once an ace has been drawn)

For probability that all/both are found by multiplying the individual probabilities.

4/52 * 16/51 = ?

b. 16/52 * 15/51 = ?

c. What combinations of two cards will give you 16 or less? Figure combos for 16 = 6,10; 5,9; etc.

It might be easier to calculate for values greater than 16 and subtract from 1.

Answer 2

a= 0.030
b= 0.091