Question

5.
A box contains 5 white and 7 black balls. Two successive drawn of 3 balls are made (1)
with replacement (ii) without replacement. The probability that the first draw would
produce white balls and the second draw would produce black balls are respectively
(a) 6/321 and 3/926
(b) 1/20 and 1/30
(c) 35/144 and 35/108
(d) 7/968 and 5/264​

Answer 1

Howdy buddy!

Find your answer below:

Probability of both happening =

Given : A box contains 5 white and 7 black balls. Two successive drawn of 3 balls are made (i) with replacement (ii) without replacement .

To find : The probability that the first draw would produce white balls and the second draw would produce black balls are respectively.

Solution : Probability= Favorable outcome/ Total number of outcome

A box contains 5 white and 7 black balls = 12 balls

i) On a first drawn, (with replacement)

Total number of outcome = 12

First draw would produce white balls

Probability of first drawn is  

Probability= 5/12 x 5/12 x 5/12= 125/1728

ii) On a second drawn, (without replacement)

Total number of outcome = 12

The second draw would produce black balls

Probability of second drawn is  

Probability= 7/12 x 6/11 x 5/10= 210/1320= 21/132

→ Probability of both happening = 125/1728 x 21/132 =

2625/228096

Hope it helps!

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