Case Based Questions: Probability | Mathematics (Maths) Class 10 PDF Download

Q1: Read the source below and answer the questions that follow:

i. What is the probability that a person chosen at random had type O blood? (1 mark)
ii. What is the probability that a person chosen at random had type AB blood group? (1 mark)
iii. What is the probability that a person chosen at random had neither type A nor typeB blood group? (1 mark)
iv. What is the probability that person chosen at random had either type A or type B or type O blood group? (1 mark)

Ans:
Number of people = 50
Number of people had type O blood = 21
Number of people had type A blood = 22
Number of people had type B blood = 5
Number of people had type AB blood = 50 - (21+22+5) = 50 - 48 = 2
i. Total number of possible outcomes = 50
No. of favourable outcomes = No. of people had type O blood = 21
Probability that a person chosen at random had type O blood = 21/50
ii. Total number of possible outcomes = 50
No. of favourable outcomes = No. of people had type AB blood = 2
Probability that a person chosen at random had type AB blood = 2/50
iii. Total number of possible outcomes = 50
No. of favourable outcomes = No. of people which have neither type A nor type B blood group
= 50 - (22+5) = 50 - 27 = 23
Probability that a person chosen at random had neither type A nor type B blood group = 23/50
iv. Total number of possible outcomes = 50
No. of favourable outcomes = No. of people which have either type A or type B or type O blood group.
= 22 + 5 + 21 = 48
Probability that a person chosen at random had either type A or type B or type O blood group = 48/50 = 24/25

Q2: Read the source below and answer the questions that follow:

i. Find the probability that the selected carton is of pineapple juice. (1 mark)
ii. What is the probability that selecting carton is of banana juice? (1 mark)
iii. Sunny buys 4 cartons of pineapple juice, 3 cartons of litchi juice and 3 cartons of banana juice. A customer comes to Sunny's shop and picks a tetrapack of juice at random. Find the probability that the customer picks a banana juice, if each carton has 10 tetrapacks of juice.
(1 mark)
iv. If the storekeeper bought 14 more cartons of pineapple juice, then find the probability of selecting a tetrapack of pineapple juice from the store. (1 mark)

Ans:
i. Total possible outcomes = Total number of cartons in the store
= 80 + 90 + 38 + 42 = 250
No. of favourable outcomes = No. of pineapple's cartons = 90
Probability of choosing a pineapple juice carton = 90/250 = 9/25
ii. No. of favourable outcomes = No. of banana juice cartons = 42
Probability of choosing a banana juice carton = 42/250 = 21/125
iii. Total number of cartons Sunny bought
= 4 + 3 + 3 = 10
No. of tetrapacks in 1 carton = 10
No. of favourable outcomes = 3 × 10
Total possible outcomes = Total number of tetrapacks Sunny has = 10 × 10 = 100
Probability of customer picking a banana juice tetrapack = (3 × 10) / 100 = 3/10
iv. Number of cartons left with storekeeper
= 250 - 10 = 240
Number of cartons he bought = 14
Total number of cartons with storekeeper now
= 240 + 14 = 254
Total possible outcomes = Total number of tetrapacks now = 254 × 10
No. of favourable outcomes = No. of tetrapacks of pineapple juice|= (90 - 4 + 14) × 10
Probability of selecting a tetrapack of pineapple juice from store
= (90 - 4 + 14) × 10 / (254 × 10)
= 100 / 254
= 50 / 127

Q3: Read the source below and answer the questions that follow:

i. If the probability of drawing a pink ball is twice the probability of drawing a green ball, then find the number of pink balls. (1 mark)
ii. Find the probability of drawing a ball of colour other than green colour. (1 mark)
iii. Find the probability of drawing either a green or white ball. (1 mark)
iv. What is the probability that drawn ball is neither a pink nor a white ball? (1 mark)

Ans:
i. As the total number of balls is 25 and the number of red balls + white balls is 13.
Total number of green balls + pink balls
= 25 - 13 = 12
Let the number of pink balls be x.
Then the number of green balls = 12 - x
We know, the probability of an event E is given by:
P(E) = Number of outcomes favourable to E / Total number of possible outcomes
Probability of drawing a pink ball = x/25
Probability of drawing a green ball = (12 - x)/25
It is given that, 
P (pink ball) = 2 × P (green ball)
x/25 = 2 × (12 - x)/25
x = 24 - 2x
3x = 24
x = 8
Therefore, the number of pink balls = 8
ii. From part (1), number of green balls = 4
Number of balls of colour other than green balls = 25 - 4 = 21
Probability of drawing a ball of colour other than green colour = 21/25
iii. The number of green balls = 4 and the number of white balls = 8
Total number of green balls + white balls = 4 + 8 = 12
Probability of drawing either a green or a white ball = 12/25
iv. The number of red balls = 5
The number of green balls = 4
Total number of red balls + green balls = 5 + 4 = 9
Probability of drawing neither a pink ball nor a white ball = 9/25