Question

If two dice are thrown simultaneously, then the probability of getting a doublet or a total of $6$ is

• A. $\frac{1}{3}$
• B. $\frac{5}{18}$
• C. $\frac{7}{18}$
• D. $\frac{11}{36}$

Answer 1

The correct option is B $\frac{5}{18}$

Total outcomes when rolling 2 dice = 36

probability of getting doublet = $P\left(A\right)=\left\{\right(1,1),(2,2),(3,3),(4,4),(5,5),(6,6\left)\right\}=6/36$

probability of getting sum as $6=P\left(B\right)=$

$\left\{\right(1,5),(2,4),(3,3),(4,2),(5,1\left)\right\}=5/36$

probability of getting a doublet and

total of 6 is $P(A\cap B)=\left\{\right(3,3\left)\right\}=1/36$

probability of getting a doublet or a

total of $6=P(A\cup B)=P\left(A\right)+P\left(B\right)-P(A\cap B)$

$=6/36+5/36-1/36$

$=10/36=5/18$