1. ## Hypergeometric Distribution

I would greatly appreciate if someone could help me set up and solve the following two problems.

1. If 7 cards are dealt from an ordinary deck of 52 cards, what is the probability that exactly 2 of them will be face cards? That at least 1 of them will be a queen?

Using the hypergeometric distribution formula, I said that this would be equal to 12 choose 3 divided by 52 choose 7. What am I doing wrong?

2. A random committee of size 3 is selected from 4 doctors and 2 nurses. Write a formula for the probability distribution of the random variable X representing the number of doctors on the committee. Find P(2<=X<=3).

Thanks!

2. Hello, Walcott89!

1. 7 cards are dealt from an ordinary deck of 52 cards.
(a) What is the probability that exactly 2 of them will be face cards?
There are: . ${52\choose7}$ possible outcomes.

There are: .12 Face Cards and 40 Others.

We want 2 Face Cards and 5 Others.
. . There are: . ${12\choose2}{40\choose5}$ ways.

Therefore: . $P(\text{exactly 2 Face Cards}) \;=\;\dfrac{{12\choose2}{40\choose5}}{{52\choose7} }$

[(b) What is the probability that at least 1 of them will be a Queen?
There are: 4 Queens and 48 Others.

Find the probability of no Queens.
Then we want 7 Others.
. . There are: . ${48\choose7}$ ways.
Hence: . $P(\text{no Queens}) \;=\;\frac{{48\choose7}}{{52\choose7}}$
Therefore: . $P(\text{at least one Queen}) \;\;=\;\;1 - \frac{{48\choose7}}{{52\choose7}}$

3. Originally Posted by Walcott89
I would greatly appreciate if someone could help me set up and solve the following two problems.

1. If 7 cards are dealt from an ordinary deck of 52 cards, what is the probability that exactly 2 of them will be face cards? That at least 1 of them will be a queen?

Using the hypergeometric distribution formula, I said that this would be equal to 12 choose 3 divided by 52 choose 7. What am I doing wrong?

2. A random committee of size 3 is selected from 4 doctors and 2 nurses. Write a formula for the probability distribution of the random variable X representing the number of doctors on the committee. Find P(2<=X<=3).

Thanks!

2.

you have to choose x doctors and (3-x) nurses in the sample of 3

C(3,x) C[2,(3-x)] / C(6,3)

binomial distributionmixture: Binomial distribution

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# a seven cards of dealt from an ordaniary deck of 52 playing cards .what is the probability that at least one of them will be queen

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