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## Homework Statement

Assume that there are bags of tulip bulbs in the basement, ant that they contain 25 bulbs each. yellow bags contain 20 yellow tulips and 5 red tuplips, and red bags contain 15 red and 10 yellow tulips. 60% of the bags in the basement are yellow, the others are red. One bulb is chosen at random from a random bag in the basement, and then planted

a) what is the probabilit that the tulip turns out yellow?

b) given that the tulip turns out yellow, what is the probability that it came from a yellow bag?

## Homework Equations

Let RB be redbag, YB yellowbag, RT red tulip and YT yellow tulip. Then as far as I can read from this exercise I have the following information:

P(YB)=0.6

P(RB)=0.4

P(YT|YB)=20/25=4/5

P(RT|YB)=1/5

P(YT|RB)=10/25=2/5

P(RT|RB)=3/5

## The Attempt at a Solution

a) [itex] P(YT)=P(YB\cap YT)+P(RB\cap YT)=(0.6*4/5)+(0.4*2/5)=16/25 [/itex]

b) [itex] P(YB|YT)=P(YB \cap YT)/P(YT) = (0,6*4/5)/(16/25)=3/4 [/itex]

It is particularly this last one I am unsure about.