Class 10 Maths Chapter 14 Question Answers - Probability

Q1: A card is drawn at random from a well shuffled deck of playing cards. Find the probability that the card drawn is
(i) a card of spade or an ace.
(ii) a black king.
(iii) neither a jack nor a king.
(iv) either a king or a queen.
Ans: Total no. of outcomes = 52


Q2: Five cards, the ten, jack, queen, king and ace of diamonds, are well shuffled with their faces downwards. One card is then picked up at random.
(a) What is the probability that the drawn card is the queen?
(b) If the queen is drawn and put aside, and a second card is drawn, find the probability that the second card is (i) an ace (ii) a queen.
Ans: (a) Total events = 5; P(queen) = 1y/5
(b) Now total events = 4
(i) P (an ace) = 1/4
(ii) P (a queen) = 0/4 = 0 …[As there is no queen left]

Q3: All the red face cards are removed from a pack of 52 playing cards. A card is drawn at random from the remaining cards, after reshuffling them. Find the probability that the drawn card is
(i) of red colour
(ii) a queen
(iii) an ace
(iv) a face card
Ans: Total number of cards = 52
Red face cards = 6
Remaining cards = 52 – 6 = 46


Q4: Red queens and black jacks are removed from a pack of 52 playing cards. A card is drawn at random from the remaining cards, after reshuffling them. Find the probability that the drawn card is
(i) a king
(ii) of red colour
(iii) a face card
(iv) a queen
Ans:
Number of red queens = 2
Number of black jacks = 2
Remaining cards = 52 – 2 – 2 = 48


Q5: Cards numbered from 11 to 60 are kept in a box. If a card is drawn at random from the box, find the probability that the number on the drawn card is:
(i) an odd number
(ii) a perfect square number
(iii) divisible by 5
(iv) a prime number less than 20
Ans: Total number of cards = 60 – 11 + 1 = 50
(i) Odd nos, are 11, 13, 15, 17, …. 59 = 25 no.
∴ P(an odd number) = 25/50 = 1/2
(ii) Perfect square numbers are 16, 25, 36, 49 = 4 numbers
∴ P(a perfect square no.) = 4/50 = 225
(iii) “Divisible by 5” numbers are 15, 20, 25, 30, 35, 40, 45, 50, 55, 60, = 10 numbers
∴ P(divisible by 5) = 10/50 = 2/25
(iv) Prime numbers less than 20 are 2, 3, 5, 7, 11, 13, 17, 19 = 8 numbers
∴ P(a prime no. less than 20) = 8/50 = 4/25

Q6: All the black face cards are removed from a pack of 52 playing cards. The remaining cards are well shuffled and then a card is drawn at random. Find the probability of getting a:
(i) face card
(ii) red card
(iii) black card
(iv) king
Ans: Total number of cards = 52
Black face cards = 6
Remaining cards = 52 – 6 = 46


Q7: Red kings and black aces are removed from a pack of 52 cards. The remaining cards are well shuffled and then a card is drawn from it. Find the probability that the drawn card is
(i) a black face card.
(ii) a red card.
Ans: Total nos. of cards = 52
Cards removed = 2 + 2 = 4
Remaining cards = 52 – 4 = 48


Q8: All kings, queens and aces are removed from a pack of 52 cards. The remaining cards are well shuffled and then a card is drawn from it. Find the probability that the drawn card is
(i) a black face card.
(ii) a red card.
Ans: Total no. of cards = 52
No. of cards removed = (4 + 4 + 4) = 12
Remaining cards = 40


Q9: A card is drawn from a well shuffled deck of 52 cards. Find the probability of getting
(i) a king of red colour
(ii) a face card
(iii) the queen of diamonds.
Ans:
(i) Total cards in a deck = 52
Total no. of kings = 4
Total no. of red kings = 2


Q10:  Two different dice are thrown together. Find the probability that the numbers obtained have 
(i) even sum, and
(ii) even product.
Ans: Two dice can be thrown as 6 × 6 = 36 ways.