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Math Olympiad Test: Probability- 4


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10 Questions MCQ Test International Mathematics Olympiad (IMO) for Class 10 | Math Olympiad Test: Probability- 4

Math Olympiad Test: Probability- 4 for Class 10 2022 is part of International Mathematics Olympiad (IMO) for Class 10 preparation. The Math Olympiad Test: Probability- 4 questions and answers have been prepared according to the Class 10 exam syllabus.The Math Olympiad Test: Probability- 4 MCQs are made for Class 10 2022 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for Math Olympiad Test: Probability- 4 below.
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Math Olympiad Test: Probability- 4 - Question 1

There are 100 cards in a bag on which numbers from 1 to 100 are written. A card is taken out from the bag at random. Find the probability that the number on the selected card is divisible by 9 and is a perfect square.

Detailed Solution for Math Olympiad Test: Probability- 4 - Question 1

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 

Math Olympiad Test: Probability- 4 - Question 2

Three cards of spades are lost from a pack of 52 playing cards. The remaining cards were well shuffled and then a card was drawn at random from them. Find the probability that the drawn cards is of black colour.

Detailed Solution for Math Olympiad Test: Probability- 4 - Question 2

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

Math Olympiad Test: Probability- 4 - Question 3

Two dice are thrown at a time. The probability that the difference of the numbers shown on the dice is 1 is _____. 

Detailed Solution for Math Olympiad Test: Probability- 4 - Question 3

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

Math Olympiad Test: Probability- 4 - Question 4

A black die, a red die and a green die are thrown at the same time. What is the probability that the sum of three numbers that turn up is 15?

Detailed Solution for Math Olympiad Test: Probability- 4 - Question 4

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

Math Olympiad Test: Probability- 4 - Question 5

A bag contains 6 blue and 4 green marbles. If a marble is drawn at random from the bag, the probability that the marble drawn is green, is ____.

Detailed Solution for Math Olympiad Test: Probability- 4 - Question 5

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

Math Olympiad Test: Probability- 4 - Question 6

A letter is chosen at random from the letters of the word ‘ASSOCIATION’. Find the probability that the chosen letter is a vowel.

Detailed Solution for Math Olympiad Test: Probability- 4 - Question 6

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

Math Olympiad Test: Probability- 4 - Question 7

A jar contains 54 marbles each of which is blue, green or white. The probability of selecting a blue marble at random from the jar is 1/3, and the probability of selecting a green marble at random is 4/9. How many white marbles does the jar contain?

Detailed Solution for Math Olympiad Test: Probability- 4 - Question 7

 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.

Math Olympiad Test: Probability- 4 - Question 8

A game consists of tossing a one rupee coin three times and noting its outcome each time. Hanif wins if all the tosses give the same result, i.e., three heads or three tails and loses otherwise. Calculate the probability that Hanif will lose the game.

Detailed Solution for Math Olympiad Test: Probability- 4 - Question 8

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.

Math Olympiad Test: Probability- 4 - Question 9

Two customers Shyam and Ekta are visiting a particular shop in the same week (Tuesday to Saturday). Each is equally likely to visit the shop on any one day as on another. 
What is the probability that both will visit the shop on different days?

Detailed Solution for Math Olympiad Test: Probability- 4 - Question 9

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

Math Olympiad Test: Probability- 4 - Question 10

A bag contains 12 balls of two different colours, out of which x are white. One ball is drawn at random. If 6 more white balls are put in the bag, the probability of drawing a white ball now will be double to that of the previous probability of drawing a white ball. Then, the value of x is _____.

Detailed Solution for Math Olympiad Test: Probability- 4 - Question 10

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

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