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Q.

It is known that in a bag there are five balls of different colours, out of which one is red. A person, who speaks truth 3 times out of 4, draws a ball at random. The probability that he will say that the ball is red, is

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a

$\frac{7}{20}$

b

3/4

c

2/3

d

3/29

answer is D.

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Detailed Solution

Let A be the event of drawing red and E be the event that the person will say that the ball is red. Then
$\begin{array}{l} P (E) = P (A) \cdot P (\frac{E}{A}) + P (\bar{A}) \cdot P (\frac{E}{A}) \\ P (A) = \frac{1}{5}, P (\bar{A}) = \frac{4}{5} \\ = (\frac{1}{5} \times \frac{3}{4}) + (\frac{4}{5} \times \frac{1}{4}) = \frac{7}{20} \end{array}$

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