Question

Suppose that the probability function in the table below reflects the possible lifetimes (in months after emergence) for fruit flies.

(a) If we know a fruit fly died before the end of its second month, what is the probability it died in its first month?

   Round your answer to two decimal places.

   P(died in first month if it dies before the end of its second month ) =

(b) If a fruit fly makes it past its second month, what is the probability it will live more than four months?

Round your answer to two decimal places.

   P(live more than four months if it makes it past its second month ) =

Fruit fly lifetimes (in months)

x	1	2	3	4	5	6
p(x)	0.30	0.20	0.20	0.15	0.10	0.05

Answer 1

(a)

P(died in first month if it dies before the end of its second month ) = P(X = 1 | X 2)

= P(X = 1 and X 2) / P(X 2)

= P(X = 1) / P(X 2)

= P(X = 1) / [P(X = 1) + P(X = 2)]

= 0.30 / (0.30 + 0.20)

= 3/5

= 0.60

(b)

P(live more than four months if it makes it past its second month ) = P(X > 4 | X > 2)

= P(X > 4 and X > 2) / P(X > 2)

= P(X > 4) / [1 - P(X 2)]

= [P(X = 5) + P(X = 6)] / [1 - (P(X = 1) + P(X = 2)]

= (0.10 + 0.05) / (1 - (0.30 + 0.20))

= 0.15 / 0.5

= 0.30