# Probability Distribution: Cards, Cummulative Distribution

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 21?

b. What is the probability of being dealth 20?

c. Construct a chart for the cumulative distribution function. What is the probability of being dealt a 16 or less? Between 12 and 16? Between 17 and 20?

d. Find the expected value and standard deviation of a two-card hand

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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 21?

Solution. If we take 2-card hand dealt from a standard deck of 52 cards, then there are cases. To be able to get 21, one card must be an ace (there are 4 aces), and the other must be 10 (there are 4*4=16 such values). So, of 1326 cases, the number of times being dealt 21 is

4*16=64.

So, the probability of being dealt 21 is 64/1326=32/663=0.0483

b. What is the probability of being dealth 20?

Solution. If we take 2-card hand dealt from a standard deck of 52 cards, then there are cases. There are ...

#### Solution Summary

The expert examines probability distributions for cards and cumulative distributions.