Probability
Class 10th Mathematics Rajasthan Board Solution
- On tossing a dice once. What is the probability of getting a number greater…
- A coin is tossed twice. What is the probability of getting two heads?…
- A number is chosen randomly from natural numbers 1 to 17. Find the probability…
- A coin is tossed three times. Find the probability of getting all heads or all…
- Find the probability of getting only 52 Sundays in a non-leap year.…
- If P(A) = 0.65 then what is the probability of “not A”?
- Two unbiased coins are tossed simultaneously. Find the probability of getting…
- A dice is tossed twice, what is the probability of getting the sum as (i) 9…
- A bag contains 5 red and 3 white balls. A ball is drawn at random from the bag.…
- 12 defective pens are accidentally mixed with 132 good ones. It is not…
- One card is drawn from a well-shuffled deck of 52 cards. Find the probability…
Exercise 18.1
Question 1.On tossing a dice once. What is the probability of getting a number greater than 4?
Answer:
The outcomes on tossing a dice can be:
1,2,3,4,5,6.
No. of favorable outcomes = 2 (5,6)
No. of total outcomes = 6
As we know
Probability = 
⇒ Probability (Getting a number greater than 4)
= 
⇒ 
Question 2.
A coin is tossed twice. What is the probability of getting two heads?
Answer:
The outcomes on tossing a coin twice are:
HH,HT,TH,TT
No. of favorable outcomes = 1
No. of total outcomes = 4
As we know
Probability = 
⇒ Probability (Getting two heads)
= 
Question 3.
A number is chosen randomly from natural numbers 1 to 17. Find the probability that it is a prime number.
Answer:
Total prime numbers between 1 to 17 are:
2,3,5,7,11,13,17
⇒ Total prime numbers = 7
Total Number between 1 to 17 is = 17
As we know,
Probability =
⇒ Probability (chosen number is prime number)
= 
Question 4.
A coin is tossed three times. Find the probability of getting all heads or all tails.
Answer:
The outcomes on tossing a coin three times are:
HHH, HHT, HTH, HTT, THH, THT, TTH, TTT
No. of favorable outcomes = 2 (HHH,TTT)
No. of total outcomes = 8
As we know,
Probability = 
⇒ Probability (Getting all heads or all tails)
= 
=
Question 5.
Find the probability of getting only 52 Sundays in a non-leap year.
Answer:
Numbers of days in non-leap year = 365
Numbers of weeks in non-leap year = 
= 52 weeks + 1 Day
As we have to find probability of only 52 Sundays.
And 52 weeks contain 52 Sundays.
⇒ The extra day should not be Sunday
⇒ Favorable outcomes = Monday, Tuesday, Wednesday, Thursday, Friday, Saturday
And no. of total outcomes = 7
As we know,
Probability =
⇒ probability (Getting only 52 Sundays in a non-leap year)
= 
Question 6.
If P(A) = 0.65 then what is the probability of “not A”?
Answer:
As we know,
Probability (“not A”) = 1 – Probability (“A”)
⇒ Probability (“not A”) = 1 – (.65)
⇒ Probability (“Not A”) = .35
Question 7.
Two unbiased coins are tossed simultaneously. Find the probability of getting at most one tail.
Answer:
The outcomes When two unbiased coins are tossed simultaneously:
HH, HT, TH, TT
No. of favorable outcomes = 3
No. of total outcomes = 4
As we know,
Probability =
⇒ Probability (Getting at most one tail)
= 
Question 8.
A dice is tossed twice, what is the probability of getting the sum as (i) 9 (ii) 13.
Answer:
The outcomes, When a dice is tossed twice are:
(1,1), (1,2), (1,3), (1,4), (1,5), (1,6)
(2,1), (2,2), (2,3), (2,4), (2,5), (2,6)
(3,1), (3,2), (3,3), (3,4), (3,5), (3,6)
(4,1), (4,2), (4,3), (4,4), (4,5), (4,6)
(5,1), (5,2), (5,3), (5,4) (5,5), (5,6)
(6,1), (6,2), (6,3), (6,4), (6,5), (6,6)
(i) Probability of getting the sum as 9
(6,3), (5,4), (4,5), (3,6)
The no. of favorable outcomes = 4
The no. of total outcomes = 36
As we know,
Probability =
⇒ Probability (Getting the sum as 9)
= 
⇒ 
(ii) Probability of sum getting as 13
The no. of favorable outcomes = 0
The no. of total outcomes = 36
As we know,
Probability = 
⇒ Probability (Getting the sum as 13)
= 
⇒ 0
Question 9.
A bag contains 5 red and 3 white balls. A ball is drawn at random from the bag. What is the probability that the ball drawn is
(i) a white ball?
(ii) not a white ball?
Answer:
(i) The no. of white balls = 3
The no. of total balls in bag = 8
⇒ Probability (Getting a white ball)
=
⇒ 
(ii) Not a white ball or red ball
⇒ The no. of red balls = 5
The no. of total balls in bag = 8
⇒ Probability (Getting not a white ball)
=
= 
Question 10.
12 defective pens are accidentally mixed with 132 good ones. It is not possible to just look at a pen and tell whether or not it is defective. One pen is taken out at random from this lot. Determine the probability that the pen taken out is a good one.
Answer:
The no. of Good Pens = 132
The no. of total Pens = Defective Pens + Good Pens
⇒ The no. of total pens = 132 + 12
= 144
Probability (Pen taken out is Good one)
= 
= 
= 
Question 11.
One card is drawn from a well-shuffled deck of 52 cards. Find the probability of getting.
(i) a jack of red colour.
(ii) a red card
(iii) an ace of hearts.
(iv) the Queen of diamonds.
(v) a spade
Answer:
(i) The no. of jack of red colour = 2
The total no. of cards = 52
Probability (Getting a jack of red colour)
= 
⇒ 
= 
(ii) The no. of Red cards = 26
The no. of total cards = 52
Probability (Getting a red card )
= 
⇒ 
= 
(iii) The no. of ace of hearts = 1
The no. of total cards = 52
Probability (Getting an ace of hearts)
= 
= 
(iv)The no. of queen of diamonds = 1
The no. of total cards = 52
Probability (Getting the queen of diamonds)
=
=
(v)The no of Spade cards = 13
The no. of total cards = 52
Probability (Getting a Spade) =
⇒ 
=