Problem Set 5 Probability Class 10th Mathematics Part 1 MHB Solution

Problem Set 5

  1. Which number cannot represent a probability? Choose the correct alternative answer for…
  2. A die is rolled. What is the probability that the number appearing on upper face is…
  3. What is the probability of the event that a number chosen from 1 to 100 is a prime…
  4. There are 40 cards in a bag. Each bears a number from 1 to 40. One card is drawn at…
  5. If n(A) = 2, P(A) = 1/5, then n(S) = ? Choose the correct alternative answer for each…
  6. Basketball players John, Vasim, Akash were practising the ball drop in the basket. The…
  7. In a hockey team there are 6 defenders , 4 offenders and 1 goalee. Out of these, one…
  8. Joseph kept 26 cards in a cap, bearing one English alphabet on each card. One card is…
  9. A balloon vendor has 2 red, 3 blue and 4 green balloons. He wants to choose one of them…
  10. A box contains 5 red, 8 blue and 3 green pens. Rutuja wants to pick a pen at random.…
  11. Six faces of a die are as shown below. If the die is rolled once, find the probability…
  12. A box contains 30 tickets, bearing only one number from 1 to 30 on each. If one ticket…
  13. Length and breadth of a rectangular garden are 77 m and 50 m. There is a circular lake…
  14. In a game of chance, a spinning arrow comes to rest at one of the numbers 1, 2, 3, 4,…
  15. There are six cards in a box, each bearing a number from 0 to 5. Find the probability…
  16. A bag contains 3 red, 3 white and 3 green balls. One ball is taken out of the bag at…
  17. Each card bears one letter from the word ‘mathematics’ The cards are placed on a table…
  18. Out of 200 students from a school, 135 like Kabbaddi and the remaining students do not…
  19. A two digit number is to be formed from the digits 0, 1, 2, 3, 4. Repetition of the…
  20. The faces of a die bear numbers 0, 1, 2, 3, 4, 5. If the die is rolled twice, then…

Problem Set 5
Question 1.

Choose the correct alternative answer for each of the following question.

Which number cannot represent a probability?
A. 2/3

B. 1.5

C. 15%

D. 0.7


Answer:

As probability of any event lies between 0 and 1 , the answer is option B = 1.5 ,which is greater than 1.


Question 2.

Choose the correct alternative answer for each of the following question.

A die is rolled. What is the probability that the number appearing on upper face is less than 3?
A. 1/6

B. 1/3

C. 1/2

D. 0


Answer:

Favourable outcomes=(1,2)=2


Total number of outcomes=6


 Probability that the number appearing on upper face is less than 3=


Question 3.

Choose the correct alternative answer for each of the following question.

What is the probability of the event that a number chosen from 1 to 100 is a prime number?
A. 1/5

B. 6/25

C. 1/4

D. 13/50


Answer:

Favourable outcomes=24


Total number of outcomes=100


 Probability that the number a number chosen from 1 to 100 is a prime number =


Question 4.

Choose the correct alternative answer for each of the following question.

There are 40 cards in a bag. Each bears a number from 1 to 40. One card is drawn at random. What is the probability that the card bears a number which is a multiple of 5?
A. 1/5

B. 3/5

C. 4/5

D. 1/3


Answer:

Favourable outcomes=8


Total number of outcomes=40


 Probability that the the card bears a number which is a multiple of 5=


Question 5.

Choose the correct alternative answer for each of the following question.

If n(A) = 2, P(A) = 1/5, then n(S) = ?
A. 10

B. 5/2

C. 2/5

D. 1/3


Answer:

Probability, P(A)=


=


 n(S)=10


Question 6.

Basketball players John, Vasim, Akash were practising the ball drop in the basket. The probabilities of success for John, Vasim and Akash are 4/5 0.83 and 58% respectively. Who had the greatest probability of success?


Answer:

Probability of success for John=


Probability of success for Vasim = 0.83


Probability of success for Akash = 0.58


 Probability of success is highest for = Vasim



Question 7.

In a hockey team there are 6 defenders , 4 offenders and 1 goalee. Out of these, one player is to be selected randomly as a captain. Find the probability of the selection that -

(1) The goalee will be selected.

(2) A defender will be selected.


Answer:

(1) Probability of the selection that the goalee will be selected, p(G)=


p(G)=


(2) Probability of the selection that the goalee will be selected, p(D)=


p(D)=



Question 8.

Joseph kept 26 cards in a cap, bearing one English alphabet on each card. One card is drawn at random. What is the probability that the card drawn is a vowel card?


Answer:

Probability of the selection that the card drawn is a vowel card, p(V)=


p(V)=



Question 9.

A balloon vendor has 2 red, 3 blue and 4 green balloons. He wants to choose one of them at random to give it to Pranali. What is the probability of the event that Pranali gets,

(1) a red balloon

(2) a blue balloon

(3) a green balloon.


Answer:

(1) Probability that Pranali gets a red balloon, p(R)=


p(V)=


(2) Probability that Pranali gets a blue balloon, p(B)=


p(B)=


(3) Probability that Pranali gets a green balloon, p(G)=


p(G)=



Question 10.

A box contains 5 red, 8 blue and 3 green pens. Rutuja wants to pick a pen at random. What is the probability that the pen is blue?


Answer:

Probability that Rutuja picks blue pen, p(B)=


p(B)=



Question 11.

Six faces of a die are as shown below.



If the die is rolled once, find the probability of -

(1) ‘A’ appears on upper face.

(2) ‘D’ appears on upper face.


Answer:

(1) Probability that A appears on upper face, p(A)=


p(A)=


(2) Probability that D appears on upper face, p(D)=


p(D)=



Question 12.

A box contains 30 tickets, bearing only one number from 1 to 30 on each. If one ticket is drawn at random, find the probability of an event that the ticket drawn bears

(1) an odd number

(2) a complete square number.


Answer:

(1) Probability of an event that the ticket drawn bears an odd number, p(O)=


p(O)=


(2) Probability of an event that the ticket drawn bears a complete square number, p(S)=


p(S)=



Question 13.

Length and breadth of a rectangular garden are 77 m and 50 m. There is a circular lake in the garden having diameter 14 m. Due to wind, a towel from a terrace on a nearby building fell into the garden. Then find the probability of the event that it fell in the lake.



Answer:

Probability of the event that towel fell in the lake, p(E)= 


Area of lake= 


⇒ 


⇒ 


Area of garden= 


⇒ 


⇒ 


 p(E)=




Question 14.

In a game of chance, a spinning arrow comes to rest at one of the numbers 1, 2, 3, 4, 5, 6, 7, 8.

All these are equally likely outcomes.

Find the probability that it will rest at

(1) 8.

(2) an odd number.

(3) a number greater than 2.

(4) a number less than 9.



Answer:

(1) Probability that it will rest at 8= 


(2) Probability that it will rest at an odd number, p(O) = 


 p(O)=


(3) Probability that it will rest at a number greater than 2, p(E) = 


 p(E)=


(4) Probability that it will rest at a number less than 9, p(E) = 


 p(E)=



Question 15.

There are six cards in a box, each bearing a number from 0 to 5. Find the probability of each of the following events, that a card drawn shows,

(1) a natural number.

(2) a number less than 1.

(3) a whole number.

(4) a number is greater than 5.


Answer:

(1) Probability that card drawn shows natural number,


p(N) = 


 p(N)=


(2) Probability that card drawn shows a number less than 1,


p(L) = 


 p(L)=


(3) Probability that card drawn shows a whole number,


p(W) = 


 p(W)=


(4) Probability that card drawn shows a number is greater than 5,


p(W) = 


 p(W)=



Question 16.

A bag contains 3 red, 3 white and 3 green balls. One ball is taken out of the bag at random. What is the probability that the ball drawn is -

(1) red.

(2) not red

(3) either red or white.


Answer:

(1) Probability that ball drawn is red, p(R)=


p(R)=


(2) Probability that ball drawn is not red, p(N)=


p(N)=


(3) Probability that ball drawn is either red or white, p(E)=


p(E)=



Question 17.

Each card bears one letter from the word ‘mathematics’ The cards are placed on a table upside down. Find the probability that a card drawn bears the letter ‘m’.


Answer:

Probability that a card drawn bears the letter ‘m’, p(m)=


p(m)=



Question 18.

Out of 200 students from a school, 135 like Kabbaddi and the remaining students do not like the game. If one student is selected at random from all the students, find the probability that the student selected dosen't like Kabbaddi.


Answer:

Number of students who do not like Kabbaddi=200-135=65


Probability that the student selected dosen't like Kabbaddi, p(K)=


p(K)=



Question 19.

A two digit number is to be formed from the digits 0, 1, 2, 3, 4. Repetition of the digits is allowed. Find the probability that the number so formed is a -

(1) prime number

(2) multiple of 4

(3) multiple of 11.


Answer:

Sample Space, S= {10, 11, 12, 13, 14, 20, 21, 22, 23, 24, 30, 31, 32,33, 34, 40, 41, 42, 43, 44}


Number of sample points, n(S) = 20


(1) Probability that the number so formed is a prime number , p(Prime)= 6/20 = 3/10


p(Prime) = 3/10


(2) Probability that the number so formed is a multiple of 4, p(M) = 6/20 = 3/10


p(M) = 3/10


(3) Probability that the number so formed is a multiple of 11, p(M) = 4/20 = 1/5


p(M) = 1/5


Question 20.

The faces of a die bear numbers 0, 1, 2, 3, 4, 5. If the die is rolled twice, then find the probability that the product of digits on the upper face is zero.


Answer:

Case 1: The face of die have number 0 when rolled twice.


 Probability that the product of digits on the upper face is zero=



Case 2: One face of die has 0 and the other has any number from 1 to 5


 Probability that the product of digits on the upper face is zero=



 Total probability that the product of digits on the upper face is zero=




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