Question 5
There are 25 boys and 15 girls in a class, all of them are equally likely to be chosen for a contest. If two students are chosen one after the other without replacement for the contest, find probability that:
(a) two boys are chosen;
(b) a boy and a girl are chosen;
(c) two boys or two girls are chosen.
A box contains 5 red, 3 green and 4 blue identical beads. Calculate the probability that a girl takes away two red beads, one after the other, from the box.
Observation
The Chief Examiner reported that majority of the candidates’ who attempted the question did not quite understand the question. Some of the candidates treated question as if it was question on with replacement.
In part(a), they were expected to first find the total number of students in the class which gives 25 +15 = 40. P(2boys chosen) means the first be a boy and the second be a boy gives = . Therefore, P(2 boys chosen) = .
In part(b), they were expected to find the probability as P(1st a boy and 2nd a girl)or P(1st a girl and 2nd a boy). It gives = = .
Therefore P(a boy and a girl) = .
In part(c), they were expected to find the probability as as P(1st a boy and 2nd a boy)or P(1st a girl and 2nd a girl). It gives = = . Therefore, P(2 boys or 2girls) = .