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
Algebra ->
Probability-and-statistics
-> 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
Log On
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):
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.
