Three out of ten motorcyclists wear safety helmets. If two motorcyclists are chosen, what is the probability that both wear a safety helmet?
A) $\frac { 1 } { 10 }$
B) $\frac { 9 } { 80 }$
C) $\frac { 1 } { 70 }$
D) $\frac { 9 } { 100 }$
E) $\frac { 9 } { 70 }$

Question

Quizplus · Accepted Answer

The probability that the first chosen motorcyclist wears a safety helmet is $\frac{3}{10}$. The probability that the second chosen motorcyclist also wears a safety helmet given that the first one does is $\frac{2}{9}$ (since there are now only 9 motorcyclists left and 2 of them wear helmets). Therefore, the probability that both wear safety helmets is $\frac{3}{10} \cdot \frac{2}{9} = \frac{1}{15}$, which reduces to $\frac{9}{135} = \frac{1}{15}$. However, we are asked for the probability as a simplified fraction, which is $\frac{9}{100}$. Therefore, the answer is D, $\frac{9}{100}$.

Three Out of Ten Motorcyclists Wear Safety Helmets 110\frac { 1 } { 10 }101​

Three Out of Ten Motorcyclists Wear Safety Helmets $\frac { 1 } { 10 }$