Question 1

A number is chosen at random among the first 120 natural numbers. The probability of the number chosen being a multiple of 5 or 15 is?

Accepted Answer

∵ Total no. of favourable cases i,e., (5, 10, 15, 20, 25, 30, ....., 105, 110, 115, 120) = 24. ∴ Reqd . Prob = 24/120 = 1/5

Question 2

A bag contains 7 white and 9 red balls. The probability of drawing a white ball is?

Accepted Answer

No of white balls = 7 Red balls = 9 Total no. of balls = 7 + 9 = 16 Probability of drawing a white ball = 7/16

Question 3

A card is drawn from a well shuffled pack of cards. The probability of getting a queen of club or king of heart is?

Accepted Answer

Total ways = 52 There is one queen of club and one king of heart favourable ways = 1 + 1 = 2. ∴ Required probability = 2/52 = 1/26

Question 4

Find the probability that a vowel selected at random from the 5 vowels is an 'i'.?

Accepted Answer

Here, n(5) = {a, e, i,o, u} and E = Event of selecting the vowel i = {i} ∴ P(E)= n(E)/n(S) = 1/5

Question 5

If the probability that A will live 15 yr is 7/8 and that B will live 15 yr is 9/10, then what is the probability that both will live after 15 yr?

Accepted Answer

Required probability = P(A) x P(B) = (7/8) x (9/10) = 63/80

Question 6

A single letter is selected at random from the word 'PROBABILITY' . The probability that it is a vowel, is?

Accepted Answer

Total number of letters = n(S) = 11 whereas, number of vowels = n(E) = 4 ∴ Required probability = n(E)/n(s) = 4/11

Question 7

The probability of drawing a red card from a deck of playing cards is

Accepted Answer

Total number of cards n(S) = 52 Number of red cards n(E) = 26 ∴ P(E) = n(E)/n(S) = 26/52 = 1/2

Question 8

The probability of getting a composite number when a six-faced unbiased die is tossed, is

Accepted Answer

n(S) = 6, n(E) = (4, 6) = 2 ∴ P(E) = 2/6 = 1/3

Question 9

When two dice are rolled, what is the probability that the sum of the numbers appeared on them is 11?

Accepted Answer

n(S) = 36 n(E) = {(5,6), (6,5)} = 2 ∴ p(E) = n(E) / n(S) = 2/36 = 1/18

Question 10

Ticket numbered 1 to 20 are mixed up and then a ticket is drawn at random. What is the probability that the ticket drawn bears a number which is a multiple of 3 or 7?

Accepted Answer

Clearly, n(S) = 20 and E = { 3, 6, 9, 12, 15, 18, 7, 14 } i.e., n(E) = 8 ∴ P(E) = n(E)/ n(S) = 8/20 = 2/5

Question 11

The odds against the occurrence of an event are 5 : 4. The probability of its occurrence is?

Accepted Answer

Number of cases favourable of E = 4 Total Number of cases = (5 + 4 ) = 9 ∴ P(E) = 4/9

Question 12

A bag contains 8 red and 5 white balls. 2 balls are drawn at random. What is the probability that both are white?

Accepted Answer

n(S) = Number of ways of drawing 2 balls out of 13 = 13C2 = 13 x 12 / 2= 78 n(E) = No. of ways of drawing 2 balls out of 5 = 5C2 = 5 x 4 / 2 = 10 ∴ P(E) = n(E)/n(S) = 10/78 = 5/39

Question 13

A bag contains 6 black balls and 8 white balls. One ball is drawn at random. What is the probability that the ball drawn is white?

Accepted Answer

Total no. of balls = (6 + 8) = 14 No. of white balls = 8 ∴ P(drawing a white ball) = 8/14 = 4/7

Question 14

Three unbiased coins are tossed. What is the probability of getting at most 2 heads?

Accepted Answer

∵ n(S) = (2)3 = 8 E = Event of getting 0, or 1 or 2 heads = {TTT, TTH, THT, HTT, HHT, HTH, THH} ⇒ n(E) = 7 ∴ P(E) = n(E)/n(S) = 7/8

Question 15

Three unbiased coins are tossed, what is the probability of getting exactly two heads?

Accepted Answer

S= { HHH, HHT, HTH, THH, TTH, THT, HTT, TTT} and E = Event of getting exactly two heads = {HHT, HTH, THH} ∴ P(E) = n(E)/n(S) = 3/8

Question 16

In a simultaneous throw of two coins, the probability of getting at least one head is?

Accepted Answer

S = {HH, HT, TT, TH} and E = {HH, HT, TH } ∴ P(E) = n(E)/n(S) = 3/4

Question 17

In a throw of a coin, the probability of getting a head is?

Accepted Answer

Here S = {H, T} and E = {H} ∴ P(E) = n(E)/n(S) = 1/2

Question 18

The probability that a teacher will give one surprise test during any class meeting in a week is 1/5. If a student is absent twice. What is the probability that he will miss at least one test?

Accepted Answer

The probability of absenting of the students in the class = 2/6 = 1/3 ∴ The probability of missing his test = 1/5 x 1/3 = 1/15

Question 19

A coin is successively tossed two times. Find the probability of getting? (1) exactly one head (2)at least one head

Accepted Answer

In tossing a coin 2 times the sample space is 4 i,e (H, H), (H, T), (T, H), (T, T) (1) If A1 denotes exactly one head then A1 = {(H, T) (T, H) } So, P(A1 ) = 2/4 = 1/2 (2) If A denotes at least one head then A = {(H, T) (T, H) (H, H)} ∴ A = {(H, T) (T, H) (H, H )} ∴ P(A) = 3/4

Question 20

In a simultaneous throw of two dice find the probability of getting a total of 8 .

Accepted Answer

In a simultaneous throw of two dice Simple Space = 6 x 6 = 36 Favorable cases are = (2, 6) (3, 5) (4, 4 ) (5, 3) (6, 2) So, The required probability = 5/36

Probability Questions