faculty? (c) What is the probability of selecting a jury of two students and thr

Question

faculty? (c) What is the probability of selecting a jury of two students and three faculty? 62. Selecting a Committee Suppose that there are 55 Democrats and 45 Republicans in the U.S. Senate. A committee of seven senators is to be formed by selecting members of the Senate randomly. (a) What is the probability that the committee is composed of (d 65 to all Democrats? (b) What is the probability that the committee is composed ofo all Republicans? (c) What is the probability that the committee is composed of three Democrats and four Republicans? 63. Acceptance Sampling Suppose that a shipment of 120 electronic components contains 4 defective components. To determine whether the shipment should be accepted, a quality- control engineer randomly selects 4 of the components and them If 1 or more of the components is defective, the

Explanation / Answer

Solution:-

62)

Number of democrats = 55

Number of republicans = 45

Total number of senators = 55 + 45 = 100

a) The probability that the commitee is composed of all democrats is 0.0127.

Number of ways to select 7 senators = 100C7 = 16,007,560,800

Number of ways to select all the democrats = 55C7 = 202,927,725

The probability that the commitee is composed of all democrats = 202,927,725/16,007,560,800

The probability that the commitee is composed of all democrats = 0.0127

b) The probability that the commitee is composed of all republicans is 0.002835.

Number of ways to select 7 senators = 100C7 = 16,007,560,800

Number of ways to select all the republicans = 45C7 = 45,379,620

The probability that the commitee is composed of all republicans = 45,379,620/16,007,560,800

The probability that the commitee is composed of all republicans = 0.002835

c) The probability that the commitee is composed of three democrats and four republicans is 0.2442

Number of ways to select 7 senators = 100C7= 16,007,560,800

Number of ways to select three democrats and four republicans = 55C3 × 45C4 = 26235 × 148995 = 3,908,883,825

The probability that the commitee is composed of all republicans = 3,908,883,825/16,007,560,800

The probability that the commitee is composed of all republicans = 0.2442

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