Question

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The probability of success is 0.68. A sample of 15 is taken. Assume independent trials. (Please...

The probability of success is 0.68. A sample of 15 is taken. Assume independent trials. (Please show your work here)

1. What is the probability of succeeding all 15 times?

2. What is the probability of succeeding 9 times in 15 trials?

3. What is the probability of succeeding 14 times in 15 trials?

4. What is the probability of succeeding 12 or more times in 15 trials?

5. What is the probability of succeeding 11 or fewer times in 15 trials?

Solutions

Expert Solution

Given : n=15 , p=0.68 , q=1-p=0.32

Here ,

The probability table is ,

X
0 1 1 3.77789E-08 4E-08
1 15 0.68 1.18059E-07 1E-06
2 105 0.4624 3.68935E-07 2E-05
3 455 0.314432 1.15292E-06 0.0002
4 1365 0.21381376 3.60288E-06 0.0011
5 3003 0.145393357 1.1259E-05 0.0049
6 5005 0.098867483 3.51844E-05 0.0174
7 6435 0.067229888 0.000109951 0.0476
8 6435 0.045716324 0.000343597 0.1011
9 5005 0.0310871 0.001073742 0.1671
10 3003 0.021139228 0.003355443 0.213
11 1365 0.014374675 0.01048576 0.2057
12 455 0.009774779 0.032768 0.1457
13 105 0.00664685 0.1024 0.0715
14 15 0.004519858 0.32 0.0217
15 1 0.003073503 1 0.0031

1. The probability of succeeding all 15 times is ,

P(X=15)=0.0031

2. The probability of succeeding 9 times in 15 trials ,

P(X=9)=0.1671

3. The probability of succeeding 14 times in 15 trials is ,

P(X=14)=0.0217

4. The probability of succeeding 12 or more times in 15 trials is ,

5. The probability of succeeding 11 or fewer times in 15 trials is ,

milcah answered 1 hour ago
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