CBSE Class 10 Maths Probability

Probability

Sometimes we say, “probably it may rain” or “Probably he may get more than 90% in the examination" etc. These are elements of certainty. Means we are not certain about some things. In mathematics these comes under Probability.

The theory of probability is widely used in the area of natural as well as social science. 

Probability as a Measure of Uncertainty

Suppose we through a die which is a well balanced cube with its six faces marked numbers from 1 to 6, one number of one face, we see the number which come up on its uppermost face. A die can fall with any of its face upper most.

The number on each of the face is equally libely and possible outcome. There are six equally likely ealy outcomes: 1, 2, 3, 4, 5 or 6 in a single throw of a die. The chance of any number ‘say 3’ to come up is 1 out of 6. That is probability of 3 coming up is 1/6 i.e. p(3) = 1/6

Similarly in tossing a coin, we may get either head (H) or tail (T) up and P(H) = ½

Hence probability of an event E is

P(E) = Number of outcomes favourable to E/Total number of possible outcomes

There are only six possible outcome in a single throw of a die. If we want to find probability of 7 or 8 to come up, then in that case number of possible or favorable outcome is O (zero), hence P(7) = 0/6 = 0

i.e. probability of an impossible event is zero.

If we consider to find the probability of number less than 7, then all six cases are

favorable and hence P(number less than 7) = 6/6 = 1

i.e. probability of sure event is 1

Now, P (3) = 1/6, then probability of numbers of other than 3 must be 5/6

P(notE)=1-P(E)

Exercise - 31

1.(1) A dice is thrown once. Find the probability of getting

(a) A number greater than 3

(b) A number less than 5

2.A bag contain 5 black, 7 red and 3 white balls. A ball is drawn from the bag at random. Find the probability that the ball drawn is

(a) Red

(b) Black or white

(c) Not black.

3.A bag contains 4 red 5 black and 6 white balls. A ball is drawn from the bag a random. Find the probability that the ball drawn is

(a) White

(b) Red

(c) Not black

(d) Red or white

4.A card is drawn at random from a pack of 52 playing cards. Find the probability that the card drawn is neither a queen nor a jack.

Tickets numbered from 1 to 20 are mixed up together and then a ticket is drawn at random. What is the probability that the ticket has a number which is a multiple of 3 or 7?

In a single throw of dice, what is the probability of

(a) An odd number on one dice and 6 on the other

(b) A number greater than 4 on each dice

(c) A total of 11

(d) Getting same number on either dice.

5.A die is thrown twice. Find the probability of getting

(a) doublets

(b) number greater than 5 on one dice.

6.Three coins are tossed simultaneously. Find the probability of getting

(a) Exactly 2 heads

(b) No heads 

7.In a simultaneous toss of four coins, What is the probability of getting:

(a) Less than 2 heads?

(b) Exactly 3 head

(c) More than 2 heads? 

8.Three coins are tossed once. Find the probability of:

(a) 3 heads

(b) exactly 2 heads

(c) at least two heads

Please refer to attached file for CBSE Class 10 Maths Probability