Question

John and his brother Phil both throw a six-sided fair die. Whoever gets a 6, will win. The probability of either John or Phil win is .

• A. $\frac{1}{3}$
• B. $\frac{2}{3}$
• C. $\frac{1}{6}$

Answer 1

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

John or Phil wins for rolling $6$ in a six-sided fair die.
Number of favorable outcomes= $1$
Total number of outcomes= $6$

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

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

Now,
$\text{P (John or Phil wins)}=\text{P(John wins)}+\text{P(Phil wins)}$

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

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

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

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