Answer:
Total probability = 0.9278
Step-by-step explanation:
Probability one of the bulbs is defective = 0.1
Probability of one bulb being defective = [tex]0.1*0.9^1^4^9[/tex] * Number of possible arrangements
Probability of one bulb being defective = [tex]0.1*0.9^1^4^9 * 150[/tex]
Probability of one bulb being defective = 0.00000228
Similarly, the probability of 2 to 20 bulbs being defective can be found. We simply need to find the probability of the event happening and multiply it with the number of ways we can arrange the bulbs.
Let X be the number of defective bulbs. we then get the following equations:
Probability of event happening = 0.1 ^ (X) * 0.9 (150-X)
Arrangement (number of ways it could happen) = 150! / [ X! * (150-X)! ]
The total probability will then be the above equations multiplied. Given below are the answers for each type of event:
2 defective bulbs = 0.00001885
3 defective bulbs = 0.0001035
4 defective bulbs = 0.0004227
5 defective bulbs = 0.001371
6 defective bulbs = 0.003682
7 defective bulbs = 0.008417
8 defective bulbs = 0.01672
9 defective bulbs = 0.02931
10 defective bulbs = 0.04591
11 defective bulbs = 0.06493
12 defective bulbs = 0.08357
13 defective bulbs = 0.09857
14 defective bulbs = 0.10717
15 defective bulbs = 0.1079
16 defective bulbs = 0.1012
17 defective bulbs = 0.08865
18 defective bulbs = 0.07278
19 defective bulbs = 0.05618
20 defective bulbs = 0.04088
Adding up all the above probabilities we get the answer = 0.9278
