An unbiased die with faces marked 1, 2, 3, 4, 5 and 6 is rolled four times. Out of four face values

English

Gujarati

Hindi

14.Probability

medium

An unbiased die with faces marked $1, 2, 3, 4, 5$ and $6$ is rolled four times. Out of four face values obtained the probability that the minimum face value is not less than $2$ and the maximum face value is not greater than $5$, is

A

$16/81$

B

$ 1/81 $

C

$80/81$

D

$65/81$

(IIT-1993)

Solution

(a) $P($ minimum face value not less than $2$ and maximum face value is not greater than $5$)

$ = P(2\,{\rm{or}}\,3\,{\rm{or}}\,4\,{\rm{or}}\,5) = \frac{4}{6} = \frac{2}{3}$

Hence required probability $ = {}^4{C_4}{\left( {\frac{2}{3}} \right)^4}{\left( {\frac{1}{3}} \right)^0} = \frac{{16}}{{81}}.$

Standard 11

Mathematics

Share

Similar Questions

In an examination, there are $10$ true-false type questions. Out of $10$ , a student can guess the answer of $4$ questions correctly with probability $\frac{3}{4}$ and the remaining $6$ questions correctly with probability $\frac{1}{4}$. If the probability that the student guesses the answers of exactly $8$ questions correctly out of $10$ is $\frac{27 k }{4^{10}}$, then $k$ is equal to

hard

(JEE MAIN-2022)

In a lottery there were $90$ tickets numbered $1$ to $90$. Five tickets were drawn at random. The probability that two of the tickets drawn numbers $15$ and $89$ is

easy

A card is drawn at random from a pack of $100$ cards numbered $1$ to $100$. The probability of drawing a number which is a square is

easy

It is $5 : 2$ against a husband who is $65$ years old living till he is $85$ and $4 : 3$ against his wife who is now $58$, living till she is $78$. If the probability that atleast one of them will be alive for $20$ years, is $'k'$, then the value of $'49k'$ –

normal

If $m$ rupee coins and $n$ ten paise coins are placed in a line, then the probability that the extreme coins are ten paise coins is

hard