**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)**

$\begin{array}{l}\text{Probability(onlyonestudentischosenasaschoolprefect})\\ =\left(\frac{3}{4}\times \frac{1}{6}\right)+\left(\frac{1}{4}\times \frac{5}{6}\right)\\ =\frac{3}{24}+\frac{5}{24}\\ =\frac{1}{3}\end{array}$

**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 ⅓.

*Solution:*
Total cards in the bag =

*x*+ 6*P*(obtaining 2 green cards) = ⅓

$\begin{array}{l}\frac{6}{x+6}\times \frac{5}{x+5}=\frac{1}{3}\\ \frac{30}{\left(x+6\right)\left(x+5\right)}=\frac{1}{3}\end{array}$

(

*x*+ 6) (*x*+ 5) = 90*x*

^{2}+ 11

*x*+ 30 = 90

*x*

^{2}+ 11

*x*– 60 = 0

(

*x*– 4) (*x*+ 15) = 0

*x***= 4**or

*x*= –15 (not accepted)