Four persons are chosen at random from a group of 3 men, 2 women and 4 children. The probability of having 2 children out of 4 is :
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → \(\frac{10}{21}\)
The group has \(3+2+4=9\) persons: 4 children and 5 adults. “2 children out of 4” means the four chosen are 2 children and 2 adults; the probability is the number of such choices divided by all possible choices of 4.
All choices of 4 from 9: \(^{9}C_{4}=126\)
2 children from 4: \(^{4}C_{2}=6\); 2 adults from 5: \(^{5}C_{2}=10\)
Favourable choices \(=6\times10=60\)
Probability \(=\frac{60}{126}=\frac{10}{21}\)