The monthly worldwide average number of airplane crashes of commercial airlines is 3.5. What is the probabil - ity that there will be (a) at least 2 such accidents in the next month; (b) at most 1 accident in the next month

Step-by-step explanation:

We would apply the formula for poisson distribution which is expressed as

P (x = r) = (e^ - µ * µ^r) / r!

Where

µ represents the mean of the theoretical distribution.

r represents the number of successes of the event.

From the information given,

µ = 3.5

a)

For the probability that there will be at least 2 such accidents in the next month, it is expressed as

P (x ≥ 2) = 1 - P (x < 2)

P (x < 2) = P (x = 0) + P (x = 1)

Therefore,

P (x = 0) = (e^ - 3.5 * 3.5^0) / 0!

P (x = 0) = (e^ - 3.5 * 1) / 1

P (x = 0) = 0.03

P (x = 1) = (e^ - 3.5 * 3.5^1) / 1!

P (x = 1) = (e^ - 3.5 * 3.5) / 1

P (x = 1) = 0.11

P (x < 2) = P (x = 0) + P (x = 1) = 0.03 + 0.11 = 0.14

P (x ≥ 2) = 1 - 0.14 = 0.86

b)

For the probability that there will be at most 1 accident in the next month, it is expressed as

P (x ≤ 1) = P (x = 0) + P (x = 1)

P (x = 0) = 0.03

P (x = 1) = 0.11

P (x ≤ 1) = 0.03 + 0.11 = 0.14