An unbiased die is tossed until a number greater than 4 appears. probability that an even number of

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14.Probability

hard

An unbiased die is tossed until a number greater than $4$ appears. The probability that an even number of tosses is needed is

A

$\frac{1}{2}$

B

$\frac{2}{5}$

C

$\frac{1}{5}$

D

$\frac{2}{3}$

(IIT-1994)

Solution

(b) Probability of success $ = \frac{2}{6} = \frac{1}{3} = p$

Probability of failure $ = 1 – \frac{1}{3} = \frac{2}{3} = q$

Probability that success occurs in even number of tosses

$ = P(FS) + P(FFFS) + P(FFFFFS) + ……….$

$ = pq + {q^3}p + {q^5}p + ……..$

$ = \frac{{pq}}{{1 – {q^2}}} = \frac{2}{5}.$

Standard 11

Mathematics

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(JEE MAIN-2019)