SOLUTION: Please help me with this question: The door prizes at a dance are gift certificates from local merchants. There are four $10 certificates, five $20 certificates, and three $50 cer

Question 1117797: Please help me with this question:
The door prizes at a dance are gift certificates from local merchants. There are four $10 certificates, five $20 certificates, and three $50 certificates. The prize envelopes are mixed together in a bag and are drawn at random.
Determine the probability distribution for the number of $20 certificates in the first two prizes drawn.
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
you have:

4 ten dollar certificates
5 twenty dollar certificates
3 fifty dollar certificates.

that's a total of 12 certificates, 5 of which are twenty dollar certificates and 7 of which are not twenty dollar certificates.

you are drawing 2 times.

you can draw:

0 twenty dollar certificates on the first 2 draws.
1 twenty dollar certificate on the first draw and 0 twenty dollar certificates on the second draw.
0 twenty dollar certificates on the first draw and 1 twenty dollar certificate on the second draw.
2 twenty dollar certificates on the first 2 draws.

no other options are possible.

your probabilities will be as follows:

0 twenty dollar certificates on the first 2 draws.

the probability will be 7/12 * 6/11 = 42/132.

1 twenty dollar certificate on the first draw and 0 twenty dollar certificates on the second draw.

the probability will be 5/12 * 7/11 = 35/132.

0 twenty dollar certificates on the first draw and 1 twenty dollar certificate on the second draw.

the probability will be 7/12 * 5/11 = 35/132.

2 twenty dollar certificates on the first 2 draws.

the probability will be 5/12 * 4/11 = 20/132.

your total probabilities will be (42 + 35 + 35 + 20) / 132 = 132/132 = 1.

since the sum of all probabilities in the probability distribution must be equal to 1, then this is as it should be.

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