Q79 / 150 · MHT CET 2021 (20 Sep Shift 2) · Mathematics

Two unbiased dice are thrown. Then the probability that neither a doublet nor a total of 10 will appear is

A
$\frac{1}{12}$
B
$\frac{1}{36}$
C
$\frac{2}{9}$
Correct answer
D
$\frac{7}{9}$

Solution

Number of ways of getting doublet $=6$ Number of ways getting a total of 10 are $\Rightarrow(4,6),(5,5),(6,4)$ i.e. 3 ways Here $(5,5)$ is common. $\therefore$ Total ways of getting doublet or total of 10 are $6+3-1=8$ Hence required probability $=\frac{36-8}{36}=\frac{28}{36}=\frac{7}{9}$

Hence, the correct answer is option: 'D'.

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