Probability — Chapter Test | Class 9 IMO

Q1

Three coins are tossed. The probability of getting no tails is:

No tails means all heads {HHH}. Probability = 1/8.

Q2

A box has 90 discs (1 to 90). The probability of picking a number divisible by 5 is:

Numbers divisible by 5 up to 90 are 90 ÷ 5 = 18 numbers. Probability = 18/90 = 1/5.

Q3

A bag contains 4 red balls and 5 black balls. A ball is drawn at random. What is the probability of getting a red ball?

Total balls = 4 + 5 = 9. Red balls = 4. Probability = 4/9.

Q4

Out of 250 consecutive days, the weather forecast was correct 175 times. What is the probability that the forecast was NOT correct on a given day?

Days not correct = 250 − 175 = 75. Probability = 75/250 = 3/10.

Q5

A tyre company recorded tyre life: <4000km (20), 4000-9000km (210), 9000-14000km (325), >14000km (445). Total 1000 tyres. Probability a tyre lasts less than 4000 km is:

Tyres lasting <4000 km = 20. Total = 1000. Probability = 20/1000 = 0.02.

Q6

A letter is selected from 'ASSASSINATION'. Find the probability that the letter is 'S'.

'S' appears 4 times. Total letters = 13. Probability = 4/13.

Q7

Two fair dice are rolled together. What is the total number of possible outcomes?

Each die has 6 outcomes. For two dice, total outcomes = 6 × 6 = 36.

Q8

One card is drawn from a well-shuffled deck of 52 cards. What is the probability of getting a face card?

Face cards are King, Queen, Jack in 4 suits (total 12). Probability = 12/52 = 3/13.

Q9

The probability of an impossible event is:

An impossible event can never happen, so its number of favourable outcomes is 0. Thus, its probability is 0.

Q10

Two fair coins are tossed. What is the probability of getting at least one head?

Outcomes with at least one head = {HH, HT, TH}. Total outcomes = 4. Probability = 3/4.

Q11

The probability of a sure (or certain) event is:

A sure event always happens. The number of favourable outcomes equals the total number of outcomes, making the probability 1.

Q12

What is the probability that a non-leap year (ordinary year) contains 53 Mondays?

An ordinary year has 365 days = 52 weeks and 1 extra day. This day can be any of the 7 days of the week. Probability of it being Monday is 1/7.

Q13

A bag contains 3 red, 4 green, and 5 blue balls. One ball is drawn. What is the probability it is NOT green?

Total balls = 12. Not green means red or blue (3 + 5 = 8). Probability = 8/12 = 2/3.

Q14

A bag has 5 white, 7 red, 4 black, and 2 blue balls. Probability of drawing a white or a blue ball is:

Total balls = 5+7+4+2 = 18. White + Blue = 5 + 2 = 7. Probability = 7/18.

Q15

Two dice are rolled. What is the probability that the product of the numbers is 6?

Outcomes with product 6: (1,6), (6,1), (2,3), (3,2). Total 4. Probability = 4/36 = 1/9.