Question

If an unbiased coin is tossed and two fair dice are rolled at the same time, then what is the probability that head is the outcome and sum of the numbers on the dice is 9?

• A. $\frac{1}{2}$
• B. $\frac{1}{9}$
• C. $\frac{1}{18}$
• D. $\frac{1}{36}$

Answer 1

The correct option is C $\frac{1}{18}$

Let A be the event that coin shows head.
Let B be the event that sum of the numbers is 9.
Then$B=\left(\left(3,6\right),\left(4,5\right),\left(5,4\right),\left(6,3\right)\right\}$

Probability of getting head, $P\left(A\right)=\frac{1}{2}$
There are six possiblities for each dice.
Therefore, number of elements in the sample space for dice throw$=6\times 6=36$
$\mathrm{Therefore},P\left(B\right)=\frac{4}{36}$

Thus, probability of getting head and sum of the numbers as 9
$=\frac{1}{2}\times \frac{4}{36}=\frac{4}{72}=\frac{1}{18}$