Question

A box contains 5 red marbles, 9 blue marbles, and 11 green marbles. We draw two marbles randomly without replacement. Which ones are correct?

1. The probability that the first one is red equals .
2. The probability that the first one is red and the second one is blue equals
3. Given that the first one is NOT blue, the probability that the second marble is blue equals
4. The probability that neither is green equals

Answer 1

Red marbles = 5

Blue Marbels= 9

Green Marbels= 11

Total Marbels = 5 + 9 + 11 = 25

a) Probability (that the first one is red)= 5/25 = 1/5 = 0.2

b) Probability (that the first one is red and the second one is blue equals) = ( 5/25) * (9/24) = 3/40 = 0.075

c) P( Second marbel is Blue | Fist one is NOT Blue)

P (First one is not Blue ) = P( First one is red ) + P( First one is Green)

= ( 5/25) + ( 11/25)

= 16/25 = 0.64

P( Second marbel is Blue & First one is NOT Blue )

= P( First one is red & second one is blue ) + P( First one is green & Second one is blue)

= ( 5/25) * (9/24) + ( 11/25) * (9/24)

= 6/25 = 0.24

   P( Second marbel is Blue | Fist one is NOT Blue)

= P( Second marbel is Blue & First one is NOT Blue ) / P( First one is NOT Blue)

= 0.24/ 0.64

= 3/8

=0.375

d) P( Neither is green) = 1- P( both of them are gree)

= 1 - [ (11/25) * (10/24)]

= 1- (11/60)

= 49/60

= 0.8167