The probability that a company’s work force has no accidents in a given month is 0.7. The numbers of accidents from month to month are independent. What is the probability that the third month in a year is the first month that at least one accident occurs?

Answer :

Step 1 of 1:

From the given information the probability that a company’s workforce has no accident in a given month is 0.7.

Here A = no accident.

P(no accident) = P(A)

P(A) = 0.7

Then the number of accidents from month to month are independent.

Here B = accident

P(accident) =1-P(A)

P(B) = 1-0.7

P(B) = 0.3

Therefore the probability of accident is 0.3

Now we have to find the probability that the third month in a year is the first month that at least one accident occurs.

Then the probability that the third month in a year is the first month that at least one accident is

(No accident in first month)(No accident in second month)(No accident in third month)

= 0.70.70.3

= 0.147

Therefore the probability that the third month in a year is the first month that at least one accident occurs is 0.147