3. The names of 7 women and 3 men are written on pieces of paper and placed in a box. 4 pieces of paper are chosen randomly from the box.a. Determine the probability distribution of the number of selected papers that contain men's names:i. If they are chosen one by one without replacementii. If they are chosen one by one with replacementb. Calculate the probability that the names of at least two men are selected

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Asked Nov 13, 2019
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3. The names of 7 women and 3 men are written on pieces of paper and placed in a box. 4 pieces of paper are chosen randomly from the box.
a. Determine the probability distribution of the number of selected papers that contain men's names:
i. If they are chosen one by one without replacement
ii. If they are chosen one by one with replacement
b. Calculate the probability that the names of at least two men are selected

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Expert Answer

Step 1

From the provided information, the total names of women on paper= 7

The total names of men on paper = 3

The total number of papers (N) = 3+7 = 10

a.

The hypergeometric distribution is a discrete probability distribution which describes the probability of success in draws without replacement.

The probability distribution function of hypergeometric distribution can be written as:

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(C,)(N-Cp) n-x P(X)= Here N is the total items from whichk is the number of success, n is the item which has been drawn and x is the number of success from that.

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Step 2

i.   Consider k = 3 (number of success), if (n = 4) pieces are randomly chosen than the probability distribution of number of selected papers that contains men’s name (one by one without replacement) can be obtained as:

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(C,)(10-3C4mn,) P(X) P(x)=C.),C,) 10 C

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Step 3

ii. The probability of selecting one paper which contains men’s name with replacement p (probability of success) = 3/10

The procedure ...

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P(X-x)C,(p) (1-p)" n-x n-x 3 1 10 P(X x)=C 10

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