Question

State whether the given statement is true or false:

The probability of getting the same value on the second or third roll of a die as on the first roll is $\frac{2}{6}$.

• A. True
• B. False

Answer 1

The correct option is B

False

The probability of getting the same value on the second roll as of the first is $\frac{1}{6}$.
Similarly, the probability of getting the same value on the third roll as of the first is also $\frac{1}{6}$.
Since these are independent events, the probability of getting the same value on both the second and third roll is $\frac{1}{6}$ x $\frac{1}{6}$ = $\frac{1}{36}$.
The probability of getting the same value on either the second or third roll is $\frac{1}{6}$ + $\frac{1}{6}$ – $\frac{1}{36}$ = $\frac{11}{36}$.