Probability Worksheet Solution3





In this page probability worksheet solution3 we are going to see solution of some practice questions of the probability worksheet.

Question 7

Three coins are tossed simultaneously. Find the probability of getting    

(i) at least one head  

(ii) exactly two tails    

(iii) at least two heads

Solution:

Sample space S = {HHH, HHT, HTH, THH, HTT, THT, TTH, TTT}

n(S) = 8

(i)Let A be event of getting at least one head

A = { HHH, HHT, HTH, THH, HHT, THT, TTH}

n(A) = 7

Probability of getting at least one head, P(A) = n (A)/n(S)

                                                        P(A) = 7/8

(ii)Let B be event of getting exactly two tails

B = {HTT, THT, TTH}

n(B) = 3

Probability of getting exactly two tails, P(B) = n (B)/n(S)

                                                       P(B) = 3/8


(i) Probability of getting at least one head, P(A) = 7/8

(ii) Probability of getting exactly two tails, P(B) = 3/8


Question 8

A bag contains 6 white balls numbered from 1 to 6 and 4 red balls numbered from 7 to 10. A ball is drawn at random. Find the probability of getting

(i) an even numbered ball  

(ii)  a white ball

Solution:

Total number of balls =10

                      n(S) = 10

(i) Let A be the event of getting an even numbered ball

A = {2,4,6,8,10}

n(A) = 5

Probability of getting an even numbered ball, P(A) =  n(A)/n(S)

                                                                       = 5/10

                                                                P(A) = 1/2

(ii) Let B be the event of getting a white ball

There are 6 white balls

n(B) = 6

Probability of getting white ball, P(B) =  n(B)/n(S)

                                                    = 6/10

                                             P(B) = 3/5


(i) Probability of getting an even numbered ball, P(A) = 1/2

(ii) Probability of getting white ball, P(B) = 3/5


Question 9

A number is selected at random from integers 1 to 100. Find the probability that it is

(i) a perfect square            

(ii) not a perfect square

Solution:

Sample space = {1,2,3,4,5,…………………….100}

(i)  Let A be the event of getting a perfect square

A={1,4,9,16,25,36,49,64,81,100}

n(A) = 10

Probability of getting a perfect square number, P(A) = n(A)/n(S)

                                                                          = 10/100

                                                                          = 1/10

(ii)Let B be the event of getting not a perfect square

Probability of getting a perfect square number, P(B) = 1 - P(A)

                                                                         = 1-[1/10]

                                                                         = (10-1)/10

                                                                 P(B) = 9/10


(i) Probability of getting a perfect square number, P(A) = 1/10

(ii) Probability of getting a perfect square number, P(B) = 9/10

probability worksheet solution3 probability worksheet solution3