7.5 Probability, Short Questions (Question 1 & 2)


Question 1:
The probability of student P being chosen as a school prefect is 3 4  while the probability of student Q being chosen is 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)
Probability (both of the students are chosen as the school prefect) = 3 4 × 5 6 = 5 8

(b)
Probability (only one student is chosen as a school prefect) =( 3 4 × 1 6 )+( 1 4 × 5 6 ) = 3 24 + 5 24 = 1 3


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) =
6 x+6 × 5 x+5 = 1 3 30 ( x+6 )( x+5 ) = 1 3
(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)