CBSE Class 10 Probability Sure Shot Questions Set 09

MCQ QUESTIONS 

Question. When a die is thrown, the probability of getting an odd number less than 3 is
(a) \( 1/6 \)
(b) \( 1/3 \)
(c) \( 1/2 \)
(d) \( 0 \)
Answer: (a) \( 1/6 \)

Question. A card is drawn from a deck of 52 cards. The event E is that card is not an ace of hearts. The number of outcomes favourable to E is
(a) \( 4 \)
(b) \( 13 \)
(c) \( 48 \)
(d) \( 51 \)
Answer: (d) \( 51 \)

Question. The probability of getting a bad egg in a lot of 400 is 0.035. The number of bad eggs in the lot is
(a) \( 7 \)
(b) \( 14 \)
(c) \( 21 \)
(d) \( 28 \)
Answer: (b) \( 14 \)

Question. A girl calculates that the probability of her winning the first prize in a lottery is 0.08. If 6000 tickets are sold, how many tickets has she bought?
(a) \( 40 \)
(b) \( 240 \)
(c) \( 480 \)
(d) \( 750 \)
Answer: (c) \( 480 \)

Question. A bag has 4 red balls and 2 yellow balls. A ball is drawn from the bag without looking into the bag. What is probability of getting a red ball?
(a) \( 1/6 \)
(b) \( 2/3 \)
(c) \( 1/3 \)
(d) \( 1 \)
Answer: (b) \( 2/3 \)

Question. A coin is flipped to decide which team starts the game. What is the probability of your team will start?
(a) \( 1/4 \)
(b) \( 1/2 \)
(c) \( 1 \)
(d) \( 0 \)
Answer: (b) \( 1/2 \)

Question. One card is drawn from a well-shuffled deck of 52 cards. Find the probability of getting a king of red colour
(a) \( 1/26 \)
(b) \( 2/13 \)
(c) \( 1/13 \)
(d) \( 3/26 \)
Answer: (a) \( 1/26 \)

Question. There are 6 marbles in a box with number 1 to 6 marked on each of them. What is the probability of drawing a marble with number 2 ?
(a) \( 1/6 \)
(b) \( 1/5 \)
(c) \( 1/3 \)
(d) \( 1 \)
Answer: (a) \( 1/6 \)

Question. Find the probability that the month of April has exactly 5 Monday is
(a) \( 4/7 \)
(b) \( 5/7 \)
(c) \( 3/7 \)
(d) \( 2/7 \)
Answer: (d) \( 2/7 \)

Question. Which of the following never be the probability of an event of any random experiment.
(a) \( 112\% \)
(b) \( 7/5 \)
(c) \( -0.3\% \)
(d) All of the options
Answer: (d) All of the options

Question. Two dice are thrown at the same time, what is the probability that the sum appearing on the two top 8 is -------
(a) \( 5/8 \)
(b) \( 5/36 \)
(c) \( 5/12 \)
(d) None of the options
Answer: (b) \( 5/36 \)

Question. The probability of a sure event is -------
(a) \( 1/2 \)
(b) \( 2/3 \)
(c) \( 1 \)
(d) \( 0 \)
Answer: (c) \( 1 \)

Question. A bag contains 40 balls out of which some are red, some are blue and remaining are black. If the probability of drawing a red ball is 11/20 and that of blue ball is 1/5 , then what is the no. of black ball.
(a) \( 5 \)
(b) \( 10 \)
(c) \( 15 \)
(d) \( 20 \)
Answer: (b) \( 10 \)

Question. A card is drawn from a well shuffled deck of 52 cards. Find the probability of getting an ace.
(a) \( 1/13 \)
(b) \( 4/13 \)
(c) \( 1/52 \)
(d) \( 4/13 \)
Answer: (a) \( 1/13 \)

Question. In a lottery, there are 10 prizes and 25 blanks. Find the probability of getting a prize.
(a) \( 2/7 \)
(b) \( 5/7 \)
(c) \( 3/7 \)
(d) None of the options
Answer: (a) \( 2/7 \)

Question. Assertion: If a box contains 5 white, 2 red and 4 black marbles, then the probability of not drawing a White marble from the box is 5/11 .
Reason: \( P (\text{Not E}) = 1 - P (E) \), where E is any event.
(a) Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A).
(b) Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A).
(c) Assertion (A) is true but reason (R) is false.
(d) Assertion (A) is false but reason (R) is true
Answer: (d) Assertion (A) is false but reason (R) is true

Question. Assertion: The probability of winning a game is 0.4, then the probability of losing it, is 0.6
Reason: \( P (E) + P (\text{not E}) = 1 \)
(a) Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A).
(b) Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A).
(c) Assertion (A) is true but reason (R) is false.
(d) Assertion (A) is false but reason (R) is true
Answer: (a) Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A).

SHORT ANSWER TYPE -1  

Question. A bag contains a red ball, a blue ball and a yellow ball, all the balls being of the same size. Kritika takes out a ball from the bag without looking into it. What is the probability that she takes out the
(i) yellow ball?
(ii) red ball?
Answer: (i) \( 1/3 \), (ii) \( 1/3 \)

Question. An integer is chosen between 0 and 100. What is the probability that it is
(i) divisible by 7?
(ii) not divisible by 7?
Answer: (i) \( 14/99 \), (ii) \( 85/99 \)

Question. If \( P(E) = 0.05 \), what is the probability of ‘not E’?
Answer: \( P(\text{not E}) = 1 - 0.05 = 0.95 \)

Question. 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 is taken out is a good one.
Answer: Total pens = \( 12 + 132 = 144 \). \( P(\text{good pen}) = 132/144 = 11/12 \)

Question. There are 100 cards in a bag on which numbers from 1 to 100 are written. A card is taken out from the bag at random. Find the probability that the number on the selected card:
(i) is divisible by 9 and is a perfect square.
(ii) is a prime number greater than 80.
Answer: (i) Numbers divisible by 9 and perfect squares are 9, 36, 81. Probability = \( 3/100 \). (ii) Prime numbers > 80 are 83, 89, 97. Probability = \( 3/100 \).

Question. From a pack of 52 playing cards, Jacks, Queens and Kings of red colour are removed. From the remaining, a card is drawn at random. Find the probability that drawn card is:
1. a black king.
2. a card of red colour.
Answer: Total removed = \( 2 \text{ Jacks} + 2 \text{ Queens} + 2 \text{ Kings} = 6 \). Remaining = \( 52 - 6 = 46 \). (1) \( P(\text{black king}) = 2/46 = 1/23 \). (2) \( P(\text{red card}) = (26 - 6)/46 = 20/46 = 10/23 \).

Question. One card is drawn from a well-shuffled deck of 52 cards. Calculate the probability that the card will
(i) be an ace,
(ii) not be an ace.
Answer: (i) \( 4/52 = 1/13 \). (ii) \( 1 - 1/13 = 12/13 \).

Question. One card is drawn from a well-shuffled deck of 52 cards. Find the probability of getting
(i) red colour ace card
(ii) a face card or a spade card
Answer: (i) \( 2/52 = 1/26 \). (ii) Face cards = 12, Spades = 13. Overlap (spade face cards) = 3. Total favourable = \( 12 + 13 - 3 = 22 \). Probability = \( 22/52 = 11/26 \).

Question. Two dice are thrown at the same time. Find the probability of getting
(i) the same number on both dice.
(ii) different numbers on both dice.
Answer: (i) \( 6/36 = 1/6 \). (ii) \( 1 - 1/6 = 5/6 \).

Question. A die is thrown twice. What is the probability that
(i) 5 will not come up either time?
(ii) 5 will come up at least once?
Answer: (i) \( 25/36 \). (ii) \( 11/36 \).

Question. A coin is tossed two times. Find the probability of getting at most one head.
Answer: Outcomes: HH, HT, TH, TT. At most one head: HT, TH, TT. Probability = \( 3/4 \).