7.4 Probability II, SPM Paper 1 (Short Questions)


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
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


Question 3:
A box contains 48 marbles. There are red marbles and green marbles. A marble is chosen at random from the box. The probability that a red marble is chosen is 1 6 .
How many red marbles need to be added to the box so that the probability that a red marble is chosen is  1 2 .

Solution:
Number of red marbles in the box = 1 6 ×48 =8 Let the number of red marbles needed to be added be y. P( red marble )= 1 2 8+y 48+y = 1 2 16+2y=48+y 2yy=4816 y=32 Number of red marbles need to be added =32


Question 4:
A box contains 5 red cards, 3 yellow cards and a number of green cards. A card is picked at random from the box. Given that the probability of picking a yellow card is 1 6 , find the probability of picking a card that is not green.

Solution:
P( yellow card )= n( yellow card ) n( S )                       1 6 = 3 n( S )                 n( S )=3×6                         =18 n( not green card )=5+3=8 P( not green card )= 8 18                             = 4 9

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