What is the probability that if we choose a trinity from 19 boys and 12 girls, we will have: a) three boys b) three girls c) two boys and one girl?
Answers
Answer:
A). Total outcomes =19
A). Total outcomes =19P(3 boys) = 3/19...
A). Total outcomes =19P(3 boys) = 3/19...B) Total outcomes 12
A). Total outcomes =19P(3 boys) = 3/19...B) Total outcomes 12 P ( 3 girls) = 3/12 = 4
Given: 19 boys and 12 girls
To find: The probability of choosing a trinity where there will be:
a) three boys b) three girls c) two boys and one girl
Solution: Here to find the probability of choosing a trinity of students, we need to use combination.
a) three boys
We need to choose 3 boys out of 19 boys.
Hence, the probability of choosing a trinity where there are 3 boys
= ¹⁹C₃
= 19!/(16! × 3!)
= 969.
b) three girls
We need to choose 3 girls out of 12 girls.
Hence, the probability of choosing a trinity where there are 3 girls
= ¹²C₃
= 12!/(9! × 3!)
= 220.
c) two boys and one girl
We need to choose 2 boys out of 19 boys and 1 girl out of 12 girls.
Hence, the probability of choosing a trinity where there are two boys and one girl = ¹⁹C₂ × ¹²C₁
= 19!/(17! × 2!) × 12!/(11! × 1!)
= 171 × 12
= 2052.
Answer: a) 969
b) 220
c) 2052