7.5 Probability, Short Questions (Question 1 & 2)

Question 1:
The probability of student P being chosen as a school prefect is $\frac{3}{4}$  while the probability of student Q being chosen is $\frac{5}{6}$ .
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.

Solution:
(a)

(b)

Question 2:
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 .

Solution:
Total cards in the bag = x + 6
P(obtaining 2 green cards) =
$\begin{array}{l}\frac{6}{x+6}×\frac{5}{x+5}=\frac{1}{3}\\ \frac{30}{\left(x+6\right)\left(x+5\right)}=\frac{1}{3}\end{array}$
(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)