Test Index

NDA Math Probability

Question : 56 of 100

Marks: +1, -0

Three dice are thrown simultaneously. What is the probability that the sum on the three faces is at least 5 ?

[NDA I 2016]

$\frac{17}{18}$
$\frac{53}{54}$
$\frac{103}{108}$
$\frac{215}{216}$

Solution:

As we know that 3 dice are thrown. We want prob. of sum on three faces at least 5 i.e. some may be 5 or more. We will find prob. of sum on three faces not 5 or less, i.e. sum on faces is 3 and 4 (1,2 is not possible because of 3 dice).

No. of ways for sum on faces not 5 or more

=4

[(1,1,1),(1,2,1),(1,1,2),(2,1,1)]

Total out comes

=216

Prob. of not 5 or more

=\frac{4}{216}

Prob. of sum on three faces at least 5

1-\frac{4}{216}=\frac{212}{216}=\frac{53}{54}

Go to Question:

Prev Question

Next Question