IX Chapter-15 : PROBABILITY - NCERT solution - Key points CCE Test papers Solved Theorem and Illustrated examples

1. An activity which gives a result is called an experiment.

2. An experiment which can be repeated a number of times under the same set of conditions, and the outcomes are not predictable is called a Random Experiment.

3. Performing an experiment is called a trial.

4. Any outcome of an experiment is known as an event.

5. In n trials of a random experiments, if an event E happens m times, then the probability of happening of E is given by,

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

6. For any event E, which is associated to an experiment, we have 0 lessthan and equal P(E) greater and equalto 1.

7. If E1, E2, E3, ....., En are n elemantary events associated to a random experiment, then

P(E1) + P(E2) + P(E3) + ........... + P(En) = 1

PRACTICE EXERCISE

1. A number is chosen from 1 to 20. Find the probability that the number chosen is :

(i) a prime number (ii) a composite number

(iii) a square number (iv) an odd number

(v) an even number (vi) number between 7 and 14

2. A bag contains 9 red and 6 blue balls. Find the probability that a ball drawn from a bag at random is (i) Red ball (ii) blue ball

3. In a sample of 500 items, 120 are found to be defective. Find the probability that the item selected at random is (i) defective (ii) non-defective

4. In a school of 1800 students, there are 875 girls. Find the probability that a student chosen at random is (i) a boy (ii) a girl

5. In a cricket match, a batsman hit a boundary 12 times out 45 balls he plays. Find the probability that hedid not hit a boundary.

6. A coin is tossed 700 times and we get:

head : 385 times; tail : 315 times.

When a coin is tossed at random,what is the probability of getting : (i) a head? (ii) a tail?

7. Two coins are tossed 600 times and we get two heads : 138 times, one head : 192 times ; no head : 270times.

When two coins are tossed at random, what is the probability of getting :

(i) 2 heads? (ii) 1 head? (iii) no head?

8. Three coins are tossed 250 times and we get:

3 heads : 46 times; 2 heads : 56 times; 1 head : 70 times; 0 head : 78 times.

When three coins are tossed at random, what is the probability of getting :(i) 3 heads ? (ii) 2 heads? (iii) atleast 2 heads? (iv) atmost 2 heads?

1. An activity which gives a result is called an experiment.

2. An experiment which can be repeated a number of times under the same set of conditions, and the outcomes are not predictable is called a Random Experiment.

3. Performing an experiment is called a trial.

4. Any outcome of an experiment is known as an event.

5. In n trials of a random experiments, if an event E happens m times, then the probability of happening of E is given by,

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

6. For any event E, which is associated to an experiment, we have 0 lessthan and equal P(E) greater and equalto 1.

7. If E1, E2, E3, ....., En are n elemantary events associated to a random experiment, then

P(E1) + P(E2) + P(E3) + ........... + P(En) = 1

PRACTICE EXERCISE

1. A number is chosen from 1 to 20. Find the probability that the number chosen is :

(i) a prime number (ii) a composite number

(iii) a square number (iv) an odd number

(v) an even number (vi) number between 7 and 14

2. A bag contains 9 red and 6 blue balls. Find the probability that a ball drawn from a bag at random is (i) Red ball (ii) blue ball

3. In a sample of 500 items, 120 are found to be defective. Find the probability that the item selected at random is (i) defective (ii) non-defective

4. In a school of 1800 students, there are 875 girls. Find the probability that a student chosen at random is (i) a boy (ii) a girl

5. In a cricket match, a batsman hit a boundary 12 times out 45 balls he plays. Find the probability that hedid not hit a boundary.

6. A coin is tossed 700 times and we get:

head : 385 times; tail : 315 times.

When a coin is tossed at random,what is the probability of getting : (i) a head? (ii) a tail?

7. Two coins are tossed 600 times and we get two heads : 138 times, one head : 192 times ; no head : 270times.

When two coins are tossed at random, what is the probability of getting :

(i) 2 heads? (ii) 1 head? (iii) no head?

8. Three coins are tossed 250 times and we get:

3 heads : 46 times; 2 heads : 56 times; 1 head : 70 times; 0 head : 78 times.

When three coins are tossed at random, what is the probability of getting :(i) 3 heads ? (ii) 2 heads? (iii) atleast 2 heads? (iv) atmost 2 heads?

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