Probability 2 Short Questions (Question 1 & 2)


Question 1:
A bag contains 36 marbles which are black and white. It is given that the probability for a black marble being picked at random from the bag is   5 9 .
Calculate the number of white marbles to be taken out from the bag so that the probability of picking a black marble is   5 8 .

Solution:
Number of black marbles in the bag = 5 9 ×36=20 Let y is the total number of marbles left in the bag. y× 5 8 =20 y=20× 8 5 =32 Number of white marbles to be taken out from the bag  = 3632 =4



Question 2:
Table below shows the number of different coloured balls in three bags.


Green
Brown
Purple
Bag A
3
1
6
Bag B
5
3
4
Bag C
4
6
2 

If a bag is picked at random and then a ball is drawn randomly from that bag, what is the probability that a purple ball is drawn?

Solution:
Probability of picking a bag = 1 3
Probability of picking purple ball from bag A = 6 10 = 3 5
Probability of picking purple ball from bag B = 4 12 = 1 3
Probability of picking purple ball from bag C = 2 12 = 1 6

P( purple ball )=( 1 3 × 3 5 )+( 1 3 × 1 3 )+( 1 3 × 1 6 )                             = 1 5 + 1 9 + 1 18                             = 11 30