Two persons A and B throw a (fair)die (six-faced cube with faces numbered from 1 to 6 ) alternately,

English

Gujarati

Hindi

14.Probability

normal

Two persons $A$ and $B$ throw a (fair)die (six-faced cube with faces numbered from $1$ to $6$ ) alternately, starting with $A$. The first person to get an outcome different from the previous one by the opponent wins. The probability that $B$ wins is

$\frac{5}{6}$

$\frac{6}{7}$

$\frac{7}{8}$

$\frac{8}{9}$

(KVPY-2014)

Solution

(b)

Given, Probability of win $=\frac{5}{6}$

Probability of loss $=\frac{1}{6}$

Probability of $B$ wins =

$P(B)+P(\overline{B A} B)+P(\bar{B} \bar{A} \bar{B} \bar{A} B)+\ldots$

$=\frac{5}{6}+\frac{1}{6} \times \frac{1}{6} \times \frac{5}{6}+\frac{1}{6} \times \frac{1}{6} \times \frac{1}{6} \times \frac{1}{6} \times \frac{5}{6}+\ldots$

$=\frac{5}{6}\left(1+\frac{1}{6^2}+\frac{1}{6^4}+\frac{1}{6^6}+\ldots\right)$

$=\frac{5}{6}\left(\frac{1}{1-\frac{1}{36}}\right)=\frac{30}{35}=\frac{6}{7}$

Standard 11

Mathematics

If $A$ and $B$ are two events, then the probability of the event that at most one of $A, B$ occurs, is

normal

(IIT-2002)

Two students Anil and Ashima appeared in an examination. The probability that Anil will qualify the examination is $0.05$ and that Ashima will qualify the examination is $0.10 .$ The probability that both will qualify the examination is $0.02 .$ Find the probability that Atleast one of them will not qualify the examination.

easy

If from each of the three boxes containing $3$ white and $1$ black, $2$ white and $2$ black, $1$ white and $3$ black balls, one ball is drawn at random, then the probability that $2$ white and $1$ black ball will be drawn is

hard

(IIT-1998)

In a horse race the odds in favour of three horses are $1:2 , 1:3$ and $1:4$. The probability that one of the horse will win the race is

medium

Two aeroplanes $I$ and $II$ bomb a target in succession. The probabilities of $l$ and $II$ scoring a hit correctlyare $0.3$ and $0.2,$ respectively. The second plane will bomb only if the first misses the target. The probability that the target is hit by the second plane is