Question

In a class of 56 students, some students are boys and some are girls. If the probability of selecting a boy is the same as the probability of getting at least one tail when three coins are tossed simultaneously, then the number of girls in the class is

• A. 47
• B. 48
• C. 7
• D. 15

Answer 1

The correct option is C 7

When three coins are tossed the total number of outcomes $=2^3=8$
Outcomes having no tail = 1 (HHH)
$\therefore \text{Outcomes having at least one tail}=8–1=7$
$\therefore \text{P(at least one tail)}=\frac{\text{Number of favourable outcomes}}{\text{Total number of outcomes}}$
$=\frac{7}{8}$
According to the question:
Probability of selecting a boy = Probability of getting at least one tail
$\therefore \text{P(selecting a boy)}=\frac{7}{8}$
$\Rightarrow \text{P(selecting a girl)}=1-\frac{7}{8}=\frac{1}{8}$
Let the number of girls be x.
$\therefore \text{P(selected girl)}=\frac{\text{Outcomes of selecting a girl}}{\text{Total number of students}}$
$=\frac{x}{56}$
$\Rightarrow \frac{x}{56}=\frac{1}{8}$
$\Rightarrow x=7$
Hence, the correct answer is option (c).