The sports day committee has a list of 5 girls and 3 boys who volunteered to be reserve runners. Two reserves are picked at random from the list, and the na...
Question 1 Report
The sports day committee has a list of 5 girls and 3 boys who volunteered to be reserve runners. Two reserves are picked at random from the list, and the name picked first is not put back before the second is drawn.
- Find the probability that both reserves chosen are girls. (2)
- Find the probability that the two reserves chosen are of different genders. (2)
Answer Details
This is a "without replacement" probability question: once the first reserve is picked, the list has one fewer name, which changes the probabilities for the second pick. The probabilities of consecutive events on one branch are multiplied together.
- (a) [2]. \(P(\text{girl, then girl}) = \dfrac{5}{8} \times \dfrac{4}{7} = \dfrac{20}{56} = \dfrac{5}{14}\). The denominator falls from 8 to 7 because one name has already been removed from the list of 8.
- (b) [2]. "Different genders" happens as girl-then-boy or boy-then-girl, so both mutually exclusive cases are added: \[P(\text{girl, boy}) = \frac{5}{8} \times \frac{3}{7} = \frac{15}{56}, \qquad P(\text{boy, girl}) = \frac{3}{8} \times \frac{5}{7} = \frac{15}{56}\] \[P(\text{different genders}) = \frac{15}{56} + \frac{15}{56} = \frac{30}{56} = \frac{15}{28}\] (Equivalently, working via "same gender": \(P(GG)+P(BB) = \frac{5}{14}+\frac{3}{28}=\frac{13}{28}\), so \(P(\text{different})=1-\frac{13}{28}=\frac{15}{28}\), the same result.)
Download The App On Google Playstore
Everything you need to excel in your exams
Personalized AI Learning Chat Assistant
200,000+ Exam Questions Across IGCSE, JAMB, WAEC & NECO
Over 3,900 Lesson Notes
Offline Support - Learn Anytime, Anywhere
Green Bridge Timetable
Literature Summaries & Potential Questions
Track Your Performance & Progress
In-depth Explanations for Comprehensive Learning