1. ## Probability

There are many marbles in a big box. It is known that 30% of the marbles are red, 60% are blue and the remaining 10% is not coloured.

(a) A sample of 5 marbles is picked from the box. Find the probability that this sample contains not more than 2 red marbles.

(b) Given that there are 4 coloured marbles (red or blue) in the sample, find the probability that the majority of the marbles in the sample is red.

I managed to solve (a) but how do you solve (b)???

This is conditional probability isn't it?

Thanks for your help.

2. Originally Posted by cyt91
There are many marbles in a big box. It is known that 30% of the marbles are red, 60% are blue and the remaining 10% is not coloured.

(a) A sample of 5 marbles is picked from the box. Find the probability that this sample contains not more than 2 red marbles.

(b) Given that there are 4 coloured marbles (red or blue) in the sample, find the probability that the majority of the marbles in the sample is red.

I managed to solve (a) but how do you solve (b)???

This is conditional probability isn't it?

Thanks for your help.
For (b), yes it's a conditional probability.

Let X be the random variable of the number of coloured balls drawn in the sample where X~B(5 , 0.9)

P(X=4)=5C4 x (0.9)^4 x (0.1) = 0.32805

Let Y be the random variable of the number of red balls drawn where Y~B(4 , 0.3)

In the sample of 4, there must be 3 or 4 red balls in order for it to be the majority.

P(Y)=P(Y=3)+P(Y=4)

=(0.3)^4 + 4C3 x (0.3)^3 x (0.7)

= 0.0837

Then the required probability would be 0.0837/0.32805=0.2551