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
<h3>How to find the Probability?</h3>
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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