Probability CBSE Maths

Probability

In our day-to-day life we here statements like: most probably it will rain today, chances are high that the prices of petrol will go up, I doubt that he will win the race.

The words ‘most probably’, ‘chances’, ‘doubt’ show the probability of occurrence of an event.

Experiment: An operation which can produce some well defined outcomes is called an experiment. Each outcome is called an event.

Random Experiment: An experiment in which all possible outcomes are known and the exact outcome cannot be predicted in advance, is called a random experiment.

Important information:

(i) In tossing a coin, all possible outcomes are H, T.

(ii) In tossing two coins, all possible outcomes are HH, HT, TH, TT.

(iii) On throwing a die, all possible outcomes are 1,2,3,4,5,6.

(iv) In drawing a card from a well-shuffled deck of 52 cards, number of all possible outcomes is 52.

Probability of Occurrence of an Event:

Let E be an event. Then, the probability of occurrence of E is defined as

                            (Number of favourable outcomes)

Probability (E) =--------------------------------------------------

                                (Total Number of Outcomes)

Probability CBSE Maths

(1) (i) When a coin is tossed, write all the possible outcomes.

Answer: The all possible outcomes when a coin is tossed is = H, T.

(ii) When two coins are tossed at the same time, write all the possible outcomes.

Answer: The all possible outcomes when two coins are tossed at the same time is = HH, HT, TH, TT.

(iii) When a die is thrown, write all the possible outcomes.

Answer: The all possible outcomes when a die is thrown is= 1, 2, 3, 4, 5, 6.

(iv)Write all the possible outcomes when one card is drawn at random from a well-shuffled deck of 52 cards.

Answer: The all possible outcomes when one card is drown at random from a well-shuffled deck of 52 cards is = 52.

(2) What is the probability of getting a head when we throw a single coin?

Answer: When we toss a coin, all possible outcomes are H and T.

Therefore, total number of outcomes = 2

Number of heads = 1

Probability of getting a head = (1/2)

(3) When we tossed two coins simultaneously, what are the possibilities of getting (a) two heads (b) at least 1 head.

Answer: All the possible outcomes when we tossed two coins simultaneously are TT, TH, HT, and HH.

Therefore, total number of possible outcomes =4.

(a) Number of outcomes of getting two heads (HH) = 1.

Probability of getting two heads = (1/4).

(b) Number of outcomes of getting at least 1 head = 3.

Probability of getting at least 1 head = (3/4)

(4) In a pencil box, there are 7 red pencils and 5 black pencils. They are mixed thoroughly and one pencil takes at random. What is the probability of getting (a) a red pencil (b) a black pencil?

 Answer: Total number of pencils = 7+5=12

Therefore, total number of possible outcomes = 12

(a) Number of red pencils = 7.

Probability of getting a red pencil =(7/12)

(b) Number of black pencils = 5

Probability of getting a black pencil = (5/12)

(5) In a bag, there have 5 apples, 6 oranges and 4 bananas. We can take one fruit at random. What is the probability that the fruit drawn is (i) apple (ii) orange?

Answer: Total number of fruits = 5+6+4= 15

Therefore, total possible outcomes = 15.

(a) Number of apples = 5

Probability of getting an apple = (5/15) =(1/3)

(b) Number of oranges = 6

Probability of getting an orange = (6/15) = (2/5)

(6) There are 40 surprised gift boxes. Among them, 15 boxes have gift and the others are empty. A gift box is chosen at random. What is the probability of missing a prize?

Answer: Total number of gift boxes = 40.

Therefore, total number of possible outcomes =40.

Number of empty boxes = 40-15= 25

Probability of getting an empty box = (25/40)            

                                                                 = (5/8)

(7) In a box, there are 100 apples. Among them 8 are bad. One apple is taken out at random from the box. What is the probability that the apple drawn is (i) bad   (ii) good?

Answer: Total number of apples = 100

Therefore, total number of possible outcomes = 100.

(i) Number of bad apples = 8

Probability of getting bad an apple = (8\100)

                                                                = (2/25)

(ii) Number of good apples = 100-8 = 92

Probability of getting a good apple = (92/100)

                                                               = (23/25)

(8) A die is thrown at random. What is the probability of getting (i) 4 (ii) a number greater than 3 (iii) a prime numbers    (iv) a number less than 2?

Answer: In throwing a die, all possible outcomes are 1, 2, 3, 4, 5, 6.

Therefore, total number of possible outcomes = 6

(i) Number of 4 in die = 1

Probability of getting 4 = (1/6)

(ii) The numbers greater than 3 = 4,5, 6.

Their number = 3

Probability of getting a number greater than 3 = (3/6)

                                                                                   = (1/2)       

(iii) The prime numbers = 2, 3, 5.

Their number = 3

Probability of getting prime number = (3/6)

                                                                   = (1/2)

(iv)The number less than 2 = 1

Their number = 1

Probability of getting number less than 2 = (1/6)

(9) In a survey of 150 men, it was found that 90 like cricket and 60 like football. From these men, one is chosen at random. Find the probability that the chosen men like cricket?

Answer: Total number of men = 150.

Therefore, total number of possible outcomes = 150.

Number of men like cricket = 90

Probability of getting a man like cricket = (90/150)

                                                                        = (3/5)

(10) One card is drawn at random from a well-shuffles deck of 52 cards. What is the probability that the card drawn is (a) a king (b) red queen (iii) a spade.

Answer: Total number of cards = 52.

Therefore, total number of possible outcomes =52.

(i) Number of king = 4

Probability of getting a king = (4/52)

                                                   = (1/13)

(ii) Number of red queen = 2

Probability of getting a red queen = (2/52)

                                                              = (1/26)

(iii) Number of spade = 13

Probability of getting a spade = (13/52)

                                                      = (1/4)

Probability CBSE Maths 

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