Class 10 Maths Chapter 14 Practice Question Answers - Probability

Q1. A die is thrown then find the probability of getting a perfect square.
(a) 1/3
(b) 1/2
(c) 2/3
(d) 0
Ans: (a)
Sol:
Sample space =1,2,3,4,5,6
A perfect square in samples=1,4=2
Probability of getting perfect square = 2/6 = 1/3

Q2. If two coins are tossed then find the probability of the event of getting one head .
(a) 1/4
(b) 1/3
(c) 1/2
(d) 3/4
Ans: (c)
Sol:
sample space is ={h,t} ,{t,h}
favourable outcomes for getting one head =2
probability (one head)= 2/4

Q3. Find the probability of getting 4 when a die is thrown once.
Sol: 
Step 1: Find the probability of getting 4.
Possible outcomes on rolling the dice are 1,2,3,4,5 and 6.
Total number of outcomes = 6
Number of favorable outcome = 1

Hence, the required probability is 1/6

Q4. In tossing a coin, the chance of throwing head and tail alternatively in 3 successive trials is
(a) 1/4
(b) 1/6
(c) 1/5
(d) 1/48
Ans: (a)
Sol:
Favourable outcomes ={HTH,THT}=2 outcomes
Total number of outcomes =8
Probability = 2/8 = 1/4

Q5. If three coins are tossed then find the probability of the events of getting exactly one tail.
(a) 1/4
(b) 3/8
(c) 1/2
(d) 5/8
Ans: (b)
Sol:
A coin tossed three times sample space =(H,H,H),(H,H,T),(H,T,H),(T,H,H),(H,T,T),(T,H,T),(T,T,H),(T,T,T)
favourable outcomes for Exactly on tail =3
Probability = 3/8

Q6. A die is thrown then find the probability of getting an odd number.
(a) 1/3
(b) 2/3
(c) 1/2
(d) None of these
Ans: (c)
Sol:
Sample space =1,2,3,4,5,6
odd nos. =1,3,5
probability of getting odd nos. =3/6 = 1/2

Q7. A card is drawn at random from well shuffled pack of 52 cards. Find the probability that the card drawn is a spade:
(a) 1/4
(b) 1/3
(c) 1/2
(d) 3/4
Ans: (a)
Sol:
Sample space =52
Event a card obtained is of spade =13(spades ,13 cards of each suits)
Probability = 13/52 = 1/4

Q8. Two coins are tossed. Find the probability that a head does not appear:
(a) 1/4
(b) 1/3
(c) 1/2
(d) 2/3
Ans: (a)
Sol:
Total number of outcomes =4(HH,HT,TH,TT)
Favourable outcomes (head does not appear) =1
Probability = 1/4

Q9. A box contains 20 cards marked with the numbers 1 to 20. One card is drawn from this box at random. What is the probability that number on the card is a multiple of 5?
(a) 1/5
(b) 2/5
(c) 3/5
(d) 4/5
Ans: (a)
Sol: 
Sample space =20
multiples of 5 are(5,10,15,20)
probability of perfect square = 4/20 = 1/5

Q10. If two coins are tossed then find the probability of the events that at the most one tail turns up
(a) 1/4
(b) 1/3
(c) 1/2
(d) 3/4
Ans: (d)
Sol:
The sample space of 2 coins tossed =(h,h),(h,t),(t,h),(t,t)
for having atmost one tail we need=(h,t),(t,h),(h,h)
Thus the probability is 3/4

Q11. If three coins are tossed then find the probability of the event of getting no tail.
(a) 1/8
(b) 1/4
(c) 3/8
(d) 1/2
Ans: (a)
Sol:
A coin tossed three times sample space = {(H,H,H),(H,H,T),(H,T,H),(T,H,H),(H,T,T),(T,H,T),(T,T,H),(T,T,T)}
Favourable outcomes for No tail = 1
Probability =1/8

Q12. A box contains 3 red, 3 white and 3 green balls. A ball is selected at random. Find the probability that the ball picked up is neither a white nor a red ball:
(a) 1/4
(b) 1/3
(c) 1/2
(d) 3/4
Ans: (b)
Sol:
Total number of outcomes =9
Favourable outcomes (the ball is neither white nor red) =3
Probability = 3/9 = 1/3

Q13. Two die are thrown find the probability of getting the sum of the numbers on their upper faces to be at most 3.
(a) 1/4
(b) 1/6
(c) 1/12
(d) 1/36
Ans: (c)
Sol:
Sample space of nos obtained is =6×6  = 36  (As two dices are independent)
Sum of nos. obtained atmost 3=(1,1),(1,2)(2,1)=3
probability of getting the event = 3/36 = 1/12

Q14. Two die are thrown. Find the probability that the number on the upper face of the first dice is less than the number on the upper face of the second dice.
(a) 1/2
(b) 7/12
(c) 1/3
(d) 5/12
Ans: (d)
Sol:
Sample space of nos obtained is =6×6    (As two dices are independent)
No. obtained on first dice is less than second =15
(if no on first dice is 1 then possibility on second dice are 5(2−6) and similarly for 2=4 , for 3=3, for 4=2, for  5=1 total 5+4+3+2+1=15)
probability of event =15/36=5/12

Q15. If two coins are tossed then find the probability of the event that no head turns up.
(a) 1/4
(b) 1/3
(c) 1/2
(d) 3/4
Ans: (a)
Sol:
2 coins tossed sample space =(h,h),(h,t),(t,h),(t,t)
have no head =1(when both tail)
probability is 1/4