Discussion
A company can complete the job in time with probability 0.8. Suppose 5 jobs are assigned then the probability that all the jobs will be completed in time is ....................... .
Answer: D
The probability is \((0.8)^{5}\).
Treating the five jobs as independent, each completed in time with probability 0.8, the probability that all five succeed is the product of the five probabilities (the binomial probability of 5 successes in 5 trials):
\[ \begin{aligned} P &= 0.8 \times 0.8 \times 0.8 \times 0.8 \times 0.8 \\ &= (0.8)^{5} \approx 0.328 \end{aligned} \]
5 × 0.8 = 4 is the expected number of jobs completed, and is not even a probability. 0.8 is the chance for one job only, and 1 would mean completion is certain.
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