A pair of dice is thrown once. What is the probability that 5 will come up at least on one die?

# A pair of dice is thrown once. What is the probability that 5 will come up at least on one die?

1. A
$\frac{13}{36}$
2. B
$\frac{5}{36}$
3. C
$\frac{1}{36}$
4. D
$\frac{11}{36}$

Fill Out the Form for Expert Academic Guidance!l

+91

Live ClassesBooksTest SeriesSelf Learning

Verify OTP Code (required)

### Solution:

Given that a pair of dice is thrown once.
We know that the probability is given as the ratio of the number of favorable outcomes with the total number of possible outcomes.
$P\left(E\right)=\frac{\mathit{Number of favourable outcomes n}\left(E\right)}{\mathit{Total possible outcomes n}\left(S\right)}$
There are 36 possible outcomes when two dies are thrown, the outcomes are,  $\left\{\left(1,1\right),\left(1,2\right),\left(1,3\right),\left(1,4\right),\left(1,5\right),\left(1,6\right),\left(2,1\right),\left(2,2\right),\left(2,3\right),\left(2,4\right),\left(2,5\right),\left(2,6\right),$
$\left(3,1\right),\left(3,2\right),\left(3,3\right),\left(3,4\right),\left(3,5\right),\left(3,6\right),\left(4,1\right),\left(4,2\right),\left(4,3\right)\left(4,4\right)\left(4,5\right),\left(4,6\right),$
$\left(51\right),\left(5,2\right),\left(5,3\right),\left(5,4\right),\left(5,5\right),\left(5,6\right),\left(6,1\right),\left(6,2\right),\left(6,3\right),\left(6,4\right)\left(6,5\right)\left(6,6\right)\right\}$
Total possible outcomes, $n\left(S\right)=36$.
Let E be the event that 5 will occur at least one die.
Favourable outcomes are:
$E=\left\{\left(5,1\right),\left(5,2\right),\left(5,3\right),\left(5,4\right),\left(5,5\right),\left(5,6\right),\left(1,5\right),\left(2,5\right),\left(3,5\right),\left(4,5\right),\left(6,5\right)\right\}$ $⇒n\left(E\right)=11$
The probability of getting 5 on at least one die is,
$P\left(E\right)=\frac{\mathit{Number of favourable outcomes n}\left(E\right)}{\mathit{Total number of outcomes n}\left(S\right)}$
$⇒P\left(E\right)=\frac{11}{36}$ Therefore, the probability of getting 5 on at least one die is $\frac{11}{36}$.
Hence, option 4 is correct.

## Related content

 Matrices and Determinants_mathematics Critical Points Solved Examples Type of relations_mathematics

+91

Live ClassesBooksTest SeriesSelf Learning

Verify OTP Code (required)