find the probability

Question

Javier volunteers in community events each month. He does not do more than five events in a month. He attends exactly five events 25% of the time, four events 30% of the time, three events 25% of the time, two events 10% of the time, one event 5% of the time, and no events 5% of the time.

Find the probability that Javier volunteers for less than three events each month. (Enter an exact number as an integer, fraction, or decimal.)

P(x < 3) =

Answer 1

P(X = 5) = 0.25

P(X = 4) = 0.30

P(X = 3) = 0.25

P(X = 2) = 0.10

P(X = 1) = 0.05

P(X = 0) = 0.05

We will add up the individual probabilities up to less than 3 events.

P(X < 3) = P(X = 0) + P(X = 1) + P(X = 2) = 0.05 + 0.05 + 0.10 = 0.20

You can also use the complement rule for at least 3 events each month and still get the same answer.

P(X < 3) = 1 - P(X ≥ 3) = 1 - [P(X = 3) + P(X = 4) + P(X = 5)] = 1 - (0.25 + 0.30 + 0.25) = 1 - 0.80 = 0.20

The probability that Javier volunteers less than 3 events each month is 0.20.