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.

Answer 1

The probability that none of the prizes is a $10 gift certificate is; 7/99

The expected number of $20 gift certificates drawn is 2.083

How to find the Probability?

This is a question of picking objects from a mixture without replacement. The modelling distribution is the hypergeometric distribution, given by the formula:

P(a) = C(A,a) * C(B,b)/C(A+B,a+b)

Where;

a = number of good objects picked

b = number of bad objects picked.

A = number of good objects in the given batch.

B = number of bad objects in the given batch.

a + b = total number of objects picked without replacement.

A + B = total number of objects in the batch.

A) In this question;

A = 4 ($10, good)

B = 3 + 5 = 8 ($20, $50, "bad")

a = 0, b = 5

a + b = 5

Thus;

P(a = 0) = C(4, 0) × C(8, 5)/C(12, 5)

P(a = 0) = 1 × 56/792

P(a = 0) = 7/99

B) $20 is the "good" prize.

Thus;

A = 5

B = 3 + 4 = 7

a + b = 5 (total number of prizes drawn)

Thus;

E[$20] = (5/(5 + 3 + 4)*5)

E[$20] = (5/12)*5

E[$20] = 25/12

E[$20] = 2.083

Complete Question is;

The door prizes at a dance are four $10 gift certificates, five $20 gift certificates, and three $50 gift certificates. The prize envelopes are mixed together in a bag, and five prizes are drawn at random.

What is the probability that none of the prizes is a $10 gift certificate?

What is the expected number of $20 gift certificates drawn?

Read more about Probability at; brainly.com/question/251701

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