Question

John and his brother Alex both throw a six-sided fair die. Whoever gets a $6$, will win. What is the probability of either John or Alex win?

• A. $\frac{1}{6}$
• B. $\frac{1}{6}$
• C. $\frac{1}{3}$
• D. None of the above

Answer 1

The correct option is C $\frac{1}{3}$

$\underset{–}{\text{Given}:}$
John or his brother Alex wins for rolling $6$ in a six-sided fair die.

Number of favorable outcomes $=1$
Total number of possible outcomes $=6$

$\therefore \text{P(John wins)}=\frac{\text{Number of favorable outcomes}}{\text{Total number of possible outcomes}}=\frac{1}{6}$

Similarly, $\text{P(Alex wins)}=\frac{1}{6}$

$\underset{–}{\text{Need to Find}:}$
Probability of either John or Alex wins, i.e, $\text{P (John or Alex wins)}$

$\text{P (John or Alex wins)}=\text{P(John wins)}+\text{P(Alex wins)}$

$\Rightarrow \text{P (John or Alex wins)}=\frac{1}{6}+\frac{1}{6}$

$\Rightarrow \text{P (John or Alex wins)}=\frac{1+1}{6}=\frac{2}{6}$

$\Rightarrow \text{P (John or Alex wins)}=\frac{2\times 1}{2\times 3}=\frac{1}{3}$

$\therefore$ The probability that either John or his brother Alex wins is $\frac{1}{3}$.

Hence, option (c.) is the correct choice.