Question

Five marbles are drawn from a bag which contains 7 blue marbles and 4 blackk marbles. Find out the probability of (i) all will be blue (ii) 3 will be blue and 2 black​

Answer 1

pr(5 blue) = 1/22

Pr(3 blue, 2 black) = 5/11

Explanation:

The bag has 7 blue marbles 4 black marbles and we grab 5 out from 11 of these marbles

Probability (5 blue) = (7 choose 5)*(4 choose 0) / (11 choose 5)

This should use the combination expressions. The total number of ways to choose 5 marbles from 11 marbles is 11 choose 5. Order does not matter, so we exclude the number of permutations.

7 choose 5 = 7!/[(7-5)!*5!]= 7*6/2 = 21

4 choose 0 = 1

11 choose 5 = 11! /[ (11-5)!5!] = 11*10*9*8*7/[5*4*3*2]= 11*3*2*7

probability(5 marbles blue) = 21/(22*21) = 1/22

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Probability (3 blue , 2 black) =
(7 choose 3) (4 choose 2)/ [11 choose 5)

=(7!/[4!3!] 4!/[2!2!] )/ 77*6

=(35 *6)/ (77*6)

=5/11