A dice is rolled three times, probability of getting a larger number than previous number each time

English

Gujarati

Hindi

14.Probability

normal

A dice is rolled three times, find the probability of getting a larger number than the previous number each time ?

A

$\frac{{19}}{{216}}$

B

$\frac{{20}}{{216}}$

C

$\frac{{22}}{{216}}$

D

$\frac{{18}}{{216}}$

Solution

$P = \frac{{{\,^6}{C_3}}}{{{6^3}}} = \frac{{20}}{{216}}$

Fav Case $ = {\,^6}{{\rm{C}}_3}$ Three numbers can be selected from six number and there is only one way in which three selected number can appears.

Standard 11

Mathematics

Share

Similar Questions

A bag contains $6$ red, $5$ white and $4$ black balls. Two balls are drawn. The probability that none of them is red, is

easy

If $12$ identical balls are to be placed randomly in $3$ identical boxes, then the probability that one of the boxes contains exactly $3$ balls is

normal

If Mohan has $3$ tickets of a lottery containing $3$ prizes and $9$ blanks, then his chance of winning prize are

medium

Two squares are chosen at random on a chessboard (see figure). The probability that they have a side in common is :

hard

(JEE MAIN-2021)

In a game two players $A$ and $B$ take turns in throwing a pair of fair dice starting with player $A$ and total of scores on the two dice, in each throw is noted. $A$ wins the game if he throws a total of $6$ before $B$ throws a total of $7$ and $B$ wins the game if he throws a total of $7$ before $A$ throws a total of six The game stops as soon as either of the players wins. The probability of $A$ winning the game is

hard

(JEE MAIN-2020)