Probability — Chapter Test | Class 11 IMO

Q1

What is the probability of having exactly 53 Sundays in a leap year?

A leap year has 366 days (52 weeks + 2 days). The possible pairs for the extra days are (Sun-Mon, Mon-Tue, ..., Sat-Sun). Two out of seven pairs contain a Sunday, so the probability is 2/7.

Q2

Two dice are thrown. Number of outcomes is:

6×6=36 ordered outcomes.

Q3

A box contains tickets numbered 1 to 15. Probability of drawing a multiple of 5 is:

Multiples are 5,10,15. Thus 3/15=1/5.

Q4

A student using E-learning Hub Yudgam takes two quizzes. The probability of passing Math is 0.7, passing Physics is 0.8, and passing both is 0.6. What is the probability of passing exactly one quiz?

P(exactly one) = P(Math only) + P(Physics only) = [P(Math) − P(Both)] + [P(Physics) − P(Both)] = [0.7 − 0.6] + [0.8 − 0.6] = 0.1 + 0.2 = 0.3.

Q5

A traffic light in New Delhi is red 40% of the time, green 50% of the time, and yellow 10% of the time. What is the probability that a driver arriving randomly encounters a red or yellow light?

Being red or yellow are mutually exclusive. P(Red ∪ Yellow) = P(Red) + P(Yellow) = 0.4 + 0.1 = 0.5.

Q6

A coin is biased so that a Head is twice as likely to occur as a Tail. What is the probability of getting a Head?

Let P(Tail) = x. Then P(Head) = 2x. Since total probability is 1, x + 2x = 1, so 3x = 1, meaning x = 1/3. P(Head) = 2/3.

Q7

A die is rolled. Probability of getting a number greater than 4 is:

Numbers greater than 4 are 5 and 6. Hence 2/6 = 1/3.

Q8

A number is chosen from 1 to 30. Probability it is a prime number is:

There are 10 primes up to 30. Hence 10/30=1/3.

Q9

Which of the following represents a random experiment?

A random experiment has more than one possible outcome, and the exact outcome cannot be predicted in advance. Tossing a coin fits this definition.

Q10

A die is rolled once. The sample space has how many outcomes?

A standard die has outcomes {1,2,3,4,5,6}, so there are 6 outcomes.

Q11

If A and B are independent events, which of the following is strictly true?

By the Multiplication Law for independent events, the probability of both occurring is the product of their individual probabilities.

Q12

If P(A)=0.45 and P(B)=0.35 and A,B are mutually exclusive, then P(A')−P(B') equals:

0.55−0.65 = −0.10.

Q13

A die is biased such that any even number is thrice as likely to appear as any odd number. What is the probability of getting a 4?

Let probability of each odd number be x. P(odd) = 3x. Probability of each even is 3x. P(even) = 9x. Total = 12x = 1. So x = 1/12. Probability of getting 4 (an even number) is 3x = 3/12 = 1/4.

Q14

If P(A)=0.35, then P(A') equals:

P(A') = 1 − P(A) = 0.65.

Q15

If P(A)=3/5, then odds in favour of A are:

Odds in favour = P(A):P(A') = 3/5:2/5 = 3:2.