+91-8076753736[email protected]
logo
logo
-->

Probability

Question
CBSEENMA12033600
Wired Faculty App

A pair of dice is thrown . If the sum is seven, find the probability that one of the dice shows 3.

Solution

We have
                      straight S space equals space open curly brackets table row cell left parenthesis 1 comma space 1 right parenthesis comma end cell cell left parenthesis 1 comma space 2 right parenthesis comma end cell cell left parenthesis 1 comma space 3 right parenthesis comma end cell cell left parenthesis 1 comma space 4 right parenthesis comma end cell cell left parenthesis 1 comma space 5 right parenthesis comma end cell cell left parenthesis 1 comma space 6 right parenthesis end cell row cell left parenthesis 2 comma space 1 right parenthesis comma end cell cell left parenthesis 2 comma space 2 right parenthesis comma end cell cell left parenthesis 2 comma space 3 right parenthesis comma end cell cell left parenthesis 2 comma space 4 right parenthesis comma end cell cell left parenthesis 2 comma space 5 right parenthesis comma end cell cell left parenthesis 2 comma space 6 right parenthesis end cell row cell left parenthesis 3 comma space 1 right parenthesis comma end cell cell left parenthesis 3 comma space 2 right parenthesis comma end cell cell left parenthesis 3 comma space 3 right parenthesis comma end cell cell left parenthesis 3 comma space 4 right parenthesis comma end cell cell left parenthesis 3 comma space 5 right parenthesis comma end cell cell left parenthesis 3 comma space 6 right parenthesis end cell row cell left parenthesis 4 comma space 1 right parenthesis comma end cell cell left parenthesis 4 comma space 2 right parenthesis comma end cell cell left parenthesis 4 comma space 3 right parenthesis comma end cell cell left parenthesis 4 comma space 4 right parenthesis comma end cell cell left parenthesis 4 comma space 5 right parenthesis comma end cell cell left parenthesis 4 comma space 6 right parenthesis end cell row cell left parenthesis 5 comma space 1 right parenthesis comma end cell cell left parenthesis 5 comma space 2 right parenthesis comma end cell cell left parenthesis 5 comma space 3 right parenthesis comma end cell cell left parenthesis 5 comma space 4 right parenthesis comma end cell cell left parenthesis 5 comma space 5 right parenthesis comma end cell cell left parenthesis 5 comma space 6 right parenthesis end cell row cell left parenthesis 6 comma space 1 right parenthesis comma end cell cell left parenthesis 6 comma space 2 right parenthesis comma end cell cell left parenthesis 6 comma space 3 right parenthesis comma end cell cell left parenthesis 6 comma space 4 right parenthesis comma end cell cell left parenthesis 6 comma space 5 right parenthesis comma end cell cell left parenthesis 6 comma space 6 right parenthesis end cell end table close curly brackets
Let A = open curly brackets left parenthesis 1 comma space 3 right parenthesis comma space left parenthesis 2 comma space 3 right parenthesis comma space left parenthesis 3 comma space 1 right parenthesis comma space left parenthesis 3 comma space 2 right parenthesis comma space left parenthesis 3 comma space 4 right parenthesis comma left parenthesis 3 comma space 5 right parenthesis comma space left parenthesis 3 comma space 6 right parenthesis comma space left parenthesis 4 comma space 3 right parenthesis comma space left parenthesis 5 comma space 3 right parenthesis comma space left parenthesis 6 comma space 3 right parenthesis close curly brackets
and straight B space equals open curly brackets left parenthesis 1 comma space 6 right parenthesis comma space left parenthesis 2 comma space 5 right parenthesis comma space left parenthesis 3 comma space 4 right parenthesis comma space left parenthesis 4 comma space 3 right parenthesis comma space left parenthesis 5 comma space 2 right parenthesis comma thin space left parenthesis 6 comma space 1 right parenthesis close curly brackets
straight A intersection straight B space equals space open curly brackets left parenthesis 3 comma space 4 right parenthesis comma space space left parenthesis 4 comma space 3 right parenthesis close curly brackets
Required probability = P(A/B) = fraction numerator straight P left parenthesis straight A intersection straight B right parenthesis over denominator straight P left parenthesis straight B right parenthesis end fraction space equals fraction numerator begin display style 2 over 36 end style over denominator begin display style 6 over 36 end style end fraction space equals 1 third

Some More Questions From Probability Chapter

Mock Test Series

Mock Test Series

NCERT Sample Papers

Entrance Exams Preparation