An unbiased coin is tossed. If outcome is a head then a pair of unbiased dice is rolled and sum of n

English

Gujarati

Hindi

14.Probability

hard

An unbiased coin is tossed. If the outcome is a head then a pair of unbiased dice is rolled and the sum of the numbers obtained on the is noted. If the toss of the coin results in tail then a card from a well-shuffled pack of nine cards numbered $1, 2, 3,….., 9$ is randomly picked and the number on the card is noted. The probability that the noted number is either $7$ or $8$ is

A

$\frac{{13}}{{36}}$

B

$\frac{{15}}{{72}}$

C

$\frac{{19}}{{72}}$

D

$\frac{{19}}{{36}}$

(JEE MAIN-2019)

Solution

$\mathrm{P}(7 \text { or } 8)$

$=P(H) P(7 \text { or } 8)+P(T) P(7 \text { or } 8)$

$=\frac{1}{2} \times \frac{11}{36}+\frac{1}{2} \times \frac{2}{9}=\frac{11}{72}+\frac{1}{9}=\frac{19}{72}$

Standard 11

Mathematics

Share

Similar Questions

If $E$ and $F$ are events such that $P(E)=\frac{1}{4}$, $P(F)=\frac{1}{2}$ and $P(E$ and $F )=\frac{1}{8},$ find $:$ $P($ not $E$ and not $F)$.

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)

Check whether the following probabilities $P(A)$ and $P(B)$ are consistently defined $P ( A )=0.5$, $ P ( B )=0.4$, $P ( A \cap B )=0.8$

easy

One card is drawn at random from a well shuffled deck of $52$ cards. In which of the following cases are the events $\mathrm{E}$ and $\mathrm{F}$ independent ?

$E:$ 'the card drawn is a spade'

$F:$ 'the card drawn is an ace'

easy

The probability that a man will be alive in $20$ years is $\frac{3}{5}$ and the probability that his wife will be alive in $20$ years is $\frac{2}{3}$. Then the probability that at least one will be alive in $20$ years, is

medium