The probability of student P being chosen as a school prefect is while the probability of student Q being chosen is .
Find the probability that
(a) both of the students are chosen as the school prefect,
(b) only one student is chosen as a school prefect.
A bag contains x pink cards and 6 green cards. Two cards are drawn at random from the bag, one after the other, without replacement. Find the value of x if the probability of obtaining two green cards is ⅓.
Total cards in the bag = x + 6
P(obtaining 2 green cards) = ⅓
(x + 6) (x + 5) = 90
x2 + 11x + 30 = 90
x2 + 11x – 60 = 0
(x – 4) (x + 15) = 0
x = 4 or x = –15 (not accepted)