Math Olympiad Test: Probability- 4 - Class 10 MCQ

Total number of possible outcomes = 100
Numbers from 1 to 100 which are divisible by 9 and perfect square are 9, 36 and 81
Number of favourable outcomes = 3
∴ Required probability = 3/100 

No. of cards left = 52 - 3 = 49 
No. of cards of spade left = 13 - 3 = 10 
No. of black cards left = 13 + 10 = 23
[∵ Spade is of black colour] 
Total no. of ways to draw a card = 49 No. of ways to draw a black card = 23
∴ Required probability = 23/49

Total number of outcomes = 36
Difference of numbers is 1, when pairs are (6, 5), (5, 4), (4, 3), (3,2), (2, 1), (5, 6), (4,5), (3, 4), (2, 3), (1,2)
∴ Total favourable outcomes = 10
∴ Required probability = 10/36 = 5/18

Total number of outcomes when three dice are thrown = 6 x 6 x 6 = 216
For sum of numbers to be 15, possible ways are, (6, 6, 3), (6, 3, 6), (3, 6, 6), (6, 5, 4), (6, 4, 5), (5, 4, 6), (5, 6, 4), (4, 5, 6), (4, 6, 5), (5, 5, 5)
∴ Number of favorable outcomes = 10
∴ Required probability = 10/216 = 5/108

Total number of marbles = 10
∴ Probability of drawing a green marble = 4/10
= 2/5

Total number of letters in 'ASSOCIATION' = 11 Vowels are A, O, I, A, I, O, i.e, 6 in numbers
∴ Probability of getting a vowel =  6/11

 Let there be b blue, g green and w white marbles in the jar.
Then, b + g + w = 54   ...(i)
∴ P (Selecting a blue marble) = b/54
It is given that the probability of selecting a blue marble is 1/3
∴ 1/3 = b/54
⇒ b = 18
We have, P (Selecting a green marble) = 4/9 (given) 
⇒ g/54 = 4/9
⇒ g = 24
Substituting the values of b and g in (i), we get 18 + 24 + w = 54 ⇒ w = 12
Hence, the jar contains 12 white marbles.

We use the basic formula of favorable outcomes to solve the problem.
Total possible outcomes are = {HHH, TTT, HTH, HHT, THH, THT, TTH, HTT} = 8
Number of possible outcomes to get three heads or three tails is 2
The probability that Hanif will win the game = Number of possible outcomes/Total number of favourable outcomes
= 2/8
= 1/4
The probability that Hanif will lose the game is 1 - 1/4
= 3/4
The probability that Hanif will lose the game is 3/4.

Shyam and Ekta are visiting a shop from Tuesday to Saturday
Total possible ways of visiting the shop by them = 5 x 5 = 25
Possible ways of visiting the shop on same day = 5
∴ Possible ways of visiting the shop on different days = 25 - 5 = 20
∴ Probability o f visiting the shop on different days = 20/25 = 4/5

It is given that, total number of balls = 12
Number of white balls = x
∴ Probability of getting a white ball = x/12
Now, 6 white balls are added.
Total number of balls = 12 + 6 = 18
Number of white balls = x + 6
Probability of getting a white ball
= x + 6 / 18
According to the question,
x + 6 / 18 = 2 x x/12
⇒ x + 6 - 3x ⇒ x - 3
Number of white balls = 3