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VITEEE 2016 Paper

Section: Mathematics

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Question : 110 of 125

Marks: +1, -0

A box contains 20 identical balls of which 10 are blue and 10 are green. The balls are drawn at random from the box one at a time with replacement. The probability that a blue ball is drawn 4th time on the 7th draw is

$\frac{27}{32}$
$\frac{5}{64}$
$\frac{5}{32}$
$\frac{1}{2}$

Solution:

Probability of getting a blue ball at any draw = p =

\frac{10}{20}

=

\frac{1}{2}

P [getting a blue ball 4th time in 7th draw]

= P [getting 3 blue balls in 6 draw] x P [a blue ball in the 7th draw].

=

^{6}C_{3} \left(\frac{1}{2}\right)^3 \left(\frac{1}{2}\right)^3 \cdot \frac{1}{2}

=

\frac{6 \times 5 \times 4}{1 \times 2 \times 3} \left(\frac{1}{2}\right)^7

= 20 ×

\frac{1}{32 \times 4}

=

\frac{5}{32}

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