Question

A die is thrown three times, the probability of getting a larger number than the previous number each time, is?

• A. $\frac{5}{54}$
• B. $\frac{5}{108}$
• C. $\frac{13}{216}$
• D. None of these

Answer 1

The correct option is A $\frac{5}{54}$

Given a die is thrown 3 times.

Total number of possible outcomes $=6\times 6\times 6$

$=216$

We need number of outcomes in which we get a

larger number than the previous number each time.

The possibilities are

1 2 3 1 4 6 2 4 6

1 2 4 1 4 5 2 5 6

1 2 5 1 5 6 3 4 5

1 2 6 2 3 4 3 4 6

1 3 4 2 3 5 3 5 6

1 3 5 2 3 6 4 5 6

1 3 6 2 4 5

There are 20 possibilities.

$\therefore$ The probability $=\frac{20}{216}=\frac{5}{54}$