Selina Concise Mathematics Class 10 ICSE Solutions Chapter 25 Probability Ex 25A

These Solutions are part of Selina Concise Mathematics Class 10 ICSE Solutions. Here we have given Chapter 25 Probability Ex 25A.

Other Exercises

Question 1.
A coin is tossed once. Find the probability of:
(i) getting a tail
(ii) not getting a tail
Solution:
On tossing a coin once,
number of possible outcome = 2
(i) Favourable outome getting a tail = 1
⇒ number of favourable outcome = 2
Selina Concise Mathematics Class 10 ICSE Solutions Chapter 25 Probability Ex 25A Q1.1
(ii) Similarly favourable outcome not getting a tail = 1
But no. of possible out come = 2
Selina Concise Mathematics Class 10 ICSE Solutions Chapter 25 Probability Ex 25A Q1.2

Question 2.
A bag contains 3 white, 5 black and 2 red balls, all of the same shape and size. A ball is drawn from the bag without looking into it, find the probability that the ball drawn is :
(i) a black ball.
(ii) a red ball.
(iii) a white ball.
(iv) not a red ball.
(v) not a black ball.
Solution:
In a bag, 3 balls are white
2 balls are red
5 balls are black
Total number of balls = 3 + 2 + 5 = 10
(i) Number of possible outcome of one black ball = 10
and number of favouable outcome of one black ball = 5
Selina Concise Mathematics Class 10 ICSE Solutions Chapter 25 Probability Ex 25A Q2.1
(ii) Number of possible outcome of one red ball = 10
and number of favourable outcome = 2
Selina Concise Mathematics Class 10 ICSE Solutions Chapter 25 Probability Ex 25A Q2.2
(iii) Number of possible outcome of white ball = 10
and number of favourable outcome = 3
Selina Concise Mathematics Class 10 ICSE Solutions Chapter 25 Probability Ex 25A Q2.3
(iv) Number of possible outcome = 10
Number of favourable outcome = 3+5 = 8
not a red ball
Selina Concise Mathematics Class 10 ICSE Solutions Chapter 25 Probability Ex 25A Q2.4
(v) Number of possible outcomes =10 Number of favourable outcome
not a black ball = 3 + 2 = 5
Selina Concise Mathematics Class 10 ICSE Solutions Chapter 25 Probability Ex 25A Q2.5

Question 3.
In a single throw of a die, find the probability of getting a number :
(i) greater than 4.
(ii) less than or equal to 4.
(iii) not greater than 4.
Solution:
A die has numbers 1, 2, 3, 4, 5, 6 on its sides
∴ Number of possible outcome = 6
(i) Number of favourable outcome = greater than four i.e. two number 5 and 6
Selina Concise Mathematics Class 10 ICSE Solutions Chapter 25 Probability Ex 25A Q3.1
(ii) Number of favourable outcome = less than or equal to 4 i.e. 1, 2, 3, 4 which are 4 in number
Selina Concise Mathematics Class 10 ICSE Solutions Chapter 25 Probability Ex 25A Q3.2
(iii) Number of favourable outcome = not greater than 4 or numbers will be 1, 2, 3, 4 which are 4 in numbers
Selina Concise Mathematics Class 10 ICSE Solutions Chapter 25 Probability Ex 25A Q3.3

Question 4.
In a single throw of a die, find the probability that the number :
(i) will be an even number.
(ii) will not be an even number.
(iii) will be an odd number.
Solution:
A die has six numbers : 1, 2, 3, 4, 5, 6
∴ Number of possible outcome = 6
(i) Number of favourable outcome = an even number i.e. 2, 4, 6 which are 3 in numbers
Selina Concise Mathematics Class 10 ICSE Solutions Chapter 25 Probability Ex 25A Q4.1
(ii) & (iii) Number of favourable outcome = not an even number i.e. odd numbers : 1, 3, 5 which are 3 in numbers
Selina Concise Mathematics Class 10 ICSE Solutions Chapter 25 Probability Ex 25A Q4.2

Question 5.
From a well-shuffled deck of 52 playing-cards, one card is drawn. Find the probability that the card drawn will :
(i) be a black card.
(ii) not be a red card.
(iii) be a red card.
(iv) be a face card.
(v) be a face card of red color.
Solution:
Number of cards in a playing card deck =52
number of possible outcomes = 52
(i) Number of favourable outcomes = black cards = 26 cards
Selina Concise Mathematics Class 10 ICSE Solutions Chapter 25 Probability Ex 25A Q5.1
(ii) Number of favourable outcomes = Not be a red card = black cards = 26
Selina Concise Mathematics Class 10 ICSE Solutions Chapter 25 Probability Ex 25A Q5.2
(iii) Number of favourable outcome = Number of red cards = 26
Selina Concise Mathematics Class 10 ICSE Solutions Chapter 25 Probability Ex 25A Q5.3
(iv) Number of favourable outcome = face cards = 3×4=12
Selina Concise Mathematics Class 10 ICSE Solutions Chapter 25 Probability Ex 25A Q5.4
(v) Number of favourable outcome = face cards of red colour = 3 x2 = 6
Selina Concise Mathematics Class 10 ICSE Solutions Chapter 25 Probability Ex 25A Q5.5

Question 6.
(i) If A and B are two complementary events then what is the relation between P(A) and P(B)?
(ii) If the probability of happening of an event A is 0.46. What will be the probability of not happening of the event A ?
Solution:
(i) A and B are two complementary events
Then A = P(E) and B = P(\(\bar { E }\) )
ButP(E) + P(\(\bar { E }\)) = 1
or P(A) + P(B) = 1
(ii) ∵ P(A) + P(B) = 1 (Complementary events)
But P(A) = 0.46
∴ P(B) = 1 – P (A)
= 1 – 0.46 = 0.54

Question 7.
In a T.T. match between Geeta and Ritu, the probability of the winning of Ritu is 0.73. Find the probability of :
(i) winning of Geeta.
(ii) not winning of Ritu.
Solution:
∵ Match of T.T. is played between Geeta and Ritu
∴ Probability of winning of Geeta + Probability of winning of Ritu = 1
Probability of winning of Ritu = 0.73
(i) Probability of winning of Geeta
= 1 – probability of winning of Ritu
= 1 – 0.73 = 0.27
(ii) Probability of not winning of Ritu
= Probability of winning of Geeta = 0.27

Question 8.
In a race between Mahesh and John ; the probability that John will lose the race is 0.54.
Find the probability of :
(i) winning of Mahesh.
(ii) winning of John.
Solution:
∵ A Race is run between Mahesli and John
∴ P(E) + P(\(\bar { E }\) )=1
Where P(E) is the probability of lose the race by John
and P(\(\bar { E }\) ) is the probability of not losing or winning the race by Mahesh
But P( \(\bar { E }\) ) = 0.54
then 0.54 + P(E) = 1
⇒ P(E) = 1 – 0.54 = 0.46
∴ Probability of winning the race by John = 0.46 .

Question 9.
(i) Write the probability of a sure event.
(ii) Write the probability of an event which is impossible.
(iii) For an event E. write a relation representing the range of values of P(E).
Solution:
(i) We know that if the probability of an event is 1 then the probability is called a certain event or a sure event
Hence probability of a sure event = 1
(ii) The probability of an event which is impossible = 0
(iii) Probability of no event can be less than 0 and more than 1 and E be any event then
0 ≤ P(E) ≤ 1

Question 10.
In a single throw of a die, find the probability of getting :
(i) 5 (ii) 8
(in) a number less than 8.
(iv) a prime number.
Solution:
On a die the numbers are 1, 2, 3, 4, 5, 6 i.e. six.
∴ Number of possible outcome = 6
(i) Number of favourable outcome = 1 i.e. 5
Selina Concise Mathematics Class 10 ICSE Solutions Chapter 25 Probability Ex 25A Q10.1
(ii) Number of favourable outcome = 0 (∵ 8 is not possible)
Selina Concise Mathematics Class 10 ICSE Solutions Chapter 25 Probability Ex 25A Q10.2
(iii) Number less than 8 will be 1,2, 3, 4, 5, 6
Selina Concise Mathematics Class 10 ICSE Solutions Chapter 25 Probability Ex 25A Q10.3
(iv) A prime number will be = 2. 3, 5
Selina Concise Mathematics Class 10 ICSE Solutions Chapter 25 Probability Ex 25A Q10.4

Question 11.
A die is thrown once. Find the probability of getting :
(i) an even number.
(ii) a number between 3 and 8.
(iii) an even number or a multiple of 3.
Solution:
The number on die are 1. 2. 3. 4. 5. 6
(i) Number of even numbers on the die = 2, 4, 6 = 3
Selina Concise Mathematics Class 10 ICSE Solutions Chapter 25 Probability Ex 25A Q11.1
(ii) A number between 3 and 8 on the die = 3, 4, 5, 6 = 4
Selina Concise Mathematics Class 10 ICSE Solutions Chapter 25 Probability Ex 25A Q11.2
(iii) An even number or a multiple of 3 = 2, 3, 4, 6 = 4
Selina Concise Mathematics Class 10 ICSE Solutions Chapter 25 Probability Ex 25A Q11.3

Question 12.
Which of the following cannot be the probability of an event ?
(i) \(\frac { 3 }{ 5 }\)
(ii) 2.7
(iii) 43%
(iv) -0.6
(v) -3.2
(vi) 0.35
Solution:
We know that probability of no event can be less than 0 and more than 1
∴ If probability of any event can be less than 0 or more than 1 now
(i) \(\frac { 3 }{ 5 }\) which is between 0 and 1
∴ It is the probability of an event
(ii) 2.7 which is greater than 1
∴ It is not the probability of an event.
(iii) 43% = \(\frac { 43 }{ 100 }\) which is between 0 and 1
∴ It is the probability of an event.
(iv) -0.6 which is less than 0
∴ It is not the probability of an event
(v) -3.2 which is less than 0.
∴ It is not the probability of an event
(vi) 0.35 = \(\frac { 35 }{ 100 }\) which is between 0 and 1
∴ It is the probability of an event
Hence (ii), (iv) and (v) are not probability of an event Ans.

Question 13.
A bag contains six identical black balls. A child withdraws one ball from the bag without looking into it. What is the probability that he takes out:
(i) a white ball
(ii) a black ball
Solution:
∵ There are 6 black balls in a bag
∴ number of possible outcome = 6
(i) A white ball
As there is no white ball in the bag
∴ Its probability is zero (0) = or P(E) = 0
(ii) a black ball
∴ Number of favourable outcome = 1
Selina Concise Mathematics Class 10 ICSE Solutions Chapter 25 Probability Ex 25A Q13.1

Question 14.
A single letter is selected at random from the word ‘Probability’. Find the probability that it is a vowel.
Solution:
In the word, Probability, number of letters are
i.e. P, R, O, B, A, I, L, T, Y
and number of favourable outcome = o.a.i = 3
Selina Concise Mathematics Class 10 ICSE Solutions Chapter 25 Probability Ex 25A Q14.1

Question 15.
Ramesh chooses a date at random in January for a party (see the following figure).
Selina Concise Mathematics Class 10 ICSE Solutions Chapter 25 Probability Ex 25A Q15.1
Find the probability that he chooses :
(i) A Wednesday (ii) A Friday (iii) A Tuesday or a Saturday
Solution:
We are given the days of the month of January which has 31 days.
∴ Number of possible outcome = 31
(i) Number of Wednesday in the month = 5
Selina Concise Mathematics Class 10 ICSE Solutions Chapter 25 Probability Ex 25A Q15.2
(ii) Number of Friday in the month = 5
Selina Concise Mathematics Class 10 ICSE Solutions Chapter 25 Probability Ex 25A Q15.3
(iii) Number of Tuesday = 4
and number of Saturday = 4
Total number of Tuesday and Saturday = 4 + 4 = 8
Selina Concise Mathematics Class 10 ICSE Solutions Chapter 25 Probability Ex 25A Q15.4

Hope given Selina Concise Mathematics Class 10 ICSE Solutions Chapter 25 Probability Ex 25A are helpful to complete your math homework.

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