IX Chapter-15 : PROBABILITY - NCERT solution - Key points CCE Test papers Solved Theorem and Illustrated examples
Points to Remember :
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 : 270 times.
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?
9. Find the probability that a leap year, selected at random will have 53 sundays
10. A bag contains 10 white balls and x black balls. If the probability of drawing a black ball is double that of a white ball, find X
Points to Remember :
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 : 270 times.
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?
9. Find the probability that a leap year, selected at random will have 53 sundays
10. A bag contains 10 white balls and x black balls. If the probability of drawing a black ball is double that of a white ball, find X
