CBSE Class 10 Probability Sure Shot Questions Set 10

SHORT ANSWER TYPE

Question. Three different coins are tossed together. Find the probability of getting
(a) exactly two heads
(b) at least two heads
(c) at least two tails.
Answer: Outcomes: HHH, HHT, HTH, THH, HTT, THT, TTH, TTT (Total 8). (a) HHT, HTH, THH. Prob = \( 3/8 \). (b) HHT, HTH, THH, HHH. Prob = \( 4/8 = 1/2 \). (c) HTT, THT, TTH, TTT. Prob = \( 4/8 = 1/2 \).

Question. One 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) a red face card
Answer: (i) \( 2/52 \). (ii) \( 12/52 \). (iii) \( 6/52 \).

Question. Five cards—the ten, jack, queen, king and ace of diamonds, are removed. One card is then picked up at random.
(i) What is the probability that the card is the queen?
(ii) If the queen is drawn and put aside, what is the probability that the second card picked up is an ace?
(iii) If the ace is drawn and put aside, what is the probability that the third card picked up is ten?
Answer: (i) \( 1/5 \) (Original pool was 5 cards, but note Answer key on p.3 says \( 3/47, 3/46, 3/45 \) which implies they were drawn from a full deck of 52 after removing 5). Following Answer key: (i) \( 3/47 \), (ii) \( 3/46 \), (iii) \( 3/45 \).

Question. A box contains 12 balls out of which x are white.
(i) If one ball is drawn at random, what is the probability that it will be a white ball?
(ii) If 6 more white balls are put in the bag, the probability of drawing a white ball will be double than that in . Find x.
Answer: (i) \( x/12 \). (ii) \( x=3 \).

Question. A bag contains 5 red balls and some blue balls. If the probability of drawing blue ball is double that of a red ball, find the number of blue balls in the bag. Hence find the probability of red balls also.
Answer: Blue balls = 10, Probability of red ball = \( 1/3 \).

Question. Find the probability that a non-leap year selected at random will contain 53 Sundays.
Answer: \( 1/7 \)

Question. Find the probability that a leap year selected at random will contain 53 Tuesdays.
Answer: \( 2/7 \)

Question. Cards with numbers 2 to 101 are placed in a box. A card selected at random from the box. Find the probability that
(i) The card which is selected has a number which is a perfect square.
(ii) The card which is selected has a digit 1 at tens place.
(iii) The card which is selected has a number divisible by 7.
Answer: Total cards = 100. (i) Perfect squares (4, 9, 16, 25, 36, 49, 64, 81, 100). Prob = \( 9/100 \). (ii) Digit 1 at tens place (10-19, 110-119 is out of range). Count = 10. Prob = \( 10/100 = 1/10 \). (iii) Divisible by 7 (7, 14... 98). Count = 14. Prob = \( 14/100 \).

Question. Cards bearing numbers 4,5,6…………..,35 are kept in a bag. A card is drawn at random from the bag. Find the probability of getting a card bearing
(a) a prime number less than 15
(b) a number divisible by 3 and 5.
(c) a number whose sum of digit is divisible by 2
Answer: Total cards = 32. (a) Prime < 15: 5, 7, 11, 13. Prob = \( 4/32 = 1/8 \). (b) Divisible by 3 and 5 (i.e., 15, 30). Prob = \( 2/32 = 1/16 \). (c) Sum of digits divisible by 2. Prob = \( 17/32 \).

CASE STUDY  

Piggy bank or Money box( a coin container) is normally used by children. Piggy bank serves as a pedagogical device to teach about saving money to children. Generally, piggy banks have openings besides the slot for inserting coins but some do not have openings. We have to smash the piggy bank with a hammer or by other means, to get the money inside it. A child Shreya has a Piggybank. She saves her money in her Piggybank. One day she found that her Piggybank contains hundred 50 paisa coins, fifty 1 rupees coin, twenty 2 rupees coin, and ten 5 rupees coins. If it is equally likely that one of the coins will fall out when the bank is turned upside down.

Question. Based on the above information, answer the following questions.
(a) The probability that the fallen coin will be 50 paisa coin, is -------
(b) The probability that the fallen coin will be 5 rupees coin, is---------
(c) The probability that the fallen coin will be 2 rupees coin, is---------
(d) The probability that the fallen coin will be 2 rupees coin or 5 rupees coin, is--------
Answer: (a) \( 5/9 \), (b) \( 1/18 \), (c) \( 1/9 \), (d) \( 1/6 \)

A lottery involves the drawing of numbers at random for a prize. It is a form of gambling. Some governments have banned Lottery in their countries while some governments endorse it in their countries. there are many formats of the Lottery. In one format, the prize can be a fixed amount of cash or goods while in another format, the prize will be 50 per cent of the revenue. In a Lottery system, a box contains cards numbers between 11 to 122. A card is drawn at random from the box.

Question. Based on the above information, answer the following questions.
(a) The probability that the number on the drawn card is a square number, is:
(b) The probability that the number on the drawn card is a multiple of 7, is:
(c) The probability that the number on the drawn card is divisible by 3, is:
(d) The probability that the number on the drawn card is a multiple of 11, is:
Answer: (a) \( 4/55 \), (b) \( 8/55 \), (c) \( 5/9 \), (d) \( 37/110 \)

Most People use playing card decks just for fun and to spend time. However, there are many benefits of playing cards. It improves patience, concentration and boosts memory skills. All these help everyone in their daily life. It helps to make people socialized and help to connect with people of all mindset. Three friends play a game with playing cards. They remove Red and black colour of king , queen and ace from a pack of 52 playing cards.

Question. Based on the above information, answer the following questions.
(i) Find the probability of red colour card from the pack.
(ii) Find the probability of getting a spade.
(iii) Find the probability of getting jack of red colour.
Answer: (i) \( 1/2 \), (ii) \( 1/4 \), (iii) \( 1/20 \)

FREE TICKETS FOR WORLD CUP: Geeta wanted to watch football world cup final match. She saw an advertisement that a radio station has 25 free tickets to football world cup final match to give away. Radio announced that one participant can send only one SMS for free ticket. SMS`s are received from 20000 listeners out of which 12000 are female. SMS`s are then selected at random one at a time until all free tickets are given away.

Question. The first 24 tickets have been given away to the participants and Gita’s SMS`s has yet not been selected. What is Geeta’s chance of winning the last ticket, based on above said information.
(a) \( 1/25 \)
(b) \( 1/20000 \)
(c) \( 1/19976 \)
(d) None of the options
Answer: (b) \( 1/20000 \)

Question. Out of first 24 tickets 14 males have already won the ticket and remaining are won by females. Chances that last ticket is won by Geeta is.
(a) \( 24/25 \)
(b) \( 11990/20000 \)
(c) \( 1/19976 \)
(d) \( 11990/19976 \)
Answer: (c) \( 1/19976 \)

Question. How many more males should have sent SMS`s so that the chances of winning a ticket is equal for both male/female
(a) \( 4000 \)
(b) \( 2000 \)
(c) \( 12000 \)
(d) cannot be determined
Answer: (a) \( 4000 \)

Question. In the same condition, the number of winner tickets is doubled and one ticket is left for male while rest are won by female. Find the probability of winning last ticket by any male.
(a) \( 1/19951 \)
(b) \( 1/8000 \)
(c) \( 8000/19951 \)
(d) cannot be determined
Answer: (c) \( 8000/19951 \)

TERM INSURANCE PLAN: A particular term insurance company has two options in the application form before issuing the policy – Smoker or Non-smoker. As a smoker has more chance of getting lung disease and death chance is comparatively higher. So premium payment is more for a smoking person. Company gives a rider plan (i.e. for some critical diseases) along with normal term plan by paying some extra premium money. In a certain time period, company issues 100 policies of which 30% are for smokers and rest for non-smoker customers. Also, half the smokers and 2/5 th of non – smoking customers have purchased a rider plan along with a normal plan.

Question. Find the probability that company issues policy for a smoker with rider plan.
Answer: \( 15/100 \)

Question. Find the probability that company issues policy for a non- smoker without a rider plan.
Answer: \( 21/50 \)

Question. Find the probability that company issues policy for a smoker without a rider plan.
Answer: \( 15/100 \)

Question. Find the probability that company issues policy for a non-smoker with rider plan.
Answer: \( 7/25 \)

Playing cards: Four persons are playing a bridge game forming teams each of two players. A deck of 52 playing cards is distributed around the table clockwise in such a way that each person gets 13 cards.

Question. Find the probability of the card drawn by each player with number 5 or 6.
(a) \( 2/13 \)
(b) \( 11/13 \)
(c) \( 1/13 \)
(d) \( 12/13 \)
Answer: (a) \( 2/13 \)

Question. Find the probability of the card drawn by each player with number less than 8.
(a) \( 6/13 \)
(b) \( 5/13 \)
(c) \( 7/13 \)
(d) None of the options
Answer: (c) \( 7/13 \)

Question. Find the probability of the card drawn by each player with number between 2 and 9.
(a) \( 7/13 \)
(b) \( 5/13 \)
(c) \( 6/13 \)
(d) \( 3/13 \)
Answer: (c) \( 6/13 \)

Question. What is the probability that any one person gets queen of spade?
(a) \( 1/3 \)
(b) \( 1/4 \)
(c) \( 1/2 \)
(d) \( 1 \)
Answer: (b) \( 1/4 \)