Question

A box contain 24 identical balls of which 12 are white and 12 are black. the balls are drawn at random from the box one at a time with replacement. the probability that a white ball is drawn for the 4th time on the 7th draw is:

Answer 1

Given :

Number of balls - 24

White balls = 12

Black balls = 12

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Probability of getting a white ball and black ball -

P(white ball) = 12/24 = 1/2

P(black ball) = 12/24 = 1/2

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In the first 6 draws , we will need to get 3 white balls -

P(3 white balls in 6 draws)

= 6C3 x (1/2)^6 = 5/16 .

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Probability that the seventh draw is a white ball -

P(white ball) = 1/2

P(7th draw is a white) -

= 5/16 x 1/2 = 5/32 .

$\bold{Answer: \: Probability \: is \: 5/32}$

Answer 2

The numbers  in the series  can be multiplied  by 5 and get the next number.

So the first number can increases by the 7 for the next pair and the second number is double  for the first number.

And the answer is 4.

There are three alternatives series in each series so the numbers are data interpretation set.