### A can company reports that the number of machine breakdown in an eight hour shift has a mean of 1.5. Find the probability that there will be (i) exactly 2 breakdowns; (ii) fewer than 2 breakdowns; (iii) no breakdowns in 3 consecutive shifts.

All Probabilities are taken from the Poisson Distribution Table.
(i) exactly 2 breakdowns

P(X = 2) = 0.2510

The probability there will be exactly 2 breakdowns is 0.2510 or 25.1%

(ii) fewer than 2 breakdowns

P(X = 1) + P(X = 0)

0.3347 + 0.2233 = 0.558

The probability that there will be fewer than 2 breakdowns is 0.558 or 55.8%

(iii) no breakdowns in 3 consecutive shifts.

P(X = 0) ^ 3

0.2233 ^ 3 = 0.0111

The probability that there will be no breakdowns in 3 consecutive shifts is 0.0111 or 1.11%