# Data Handling : Exercise 5.3 (Mathematics NCERT Class 8th)

Q.1 List the outcomes you can see in these experiments.
(a) Spinning a wheel (b) Tossing two coins together
Sol. (a) For the experiment of spinning a wheel, the possible outcomes are A, B, C and D.
(b) For the experiment of two coins together, the possible outcomes are HT, TH, HH and TT where H represents Head and T represents Tail of the coins.

Q.2 When a die is thrown, list the outcomes of an event of getting
(i) (a) a prime number (b) not a prime number.
(ii) (a) a number greater than 5 (b) a number not greater than 5.
Sol. On throwing a dice, the possible outcomes are 1, 2, 3, 4, 5, and 6.
(i) (a) The outcomes of event getting a prime number are 2, 3 and 5.
(b) The outcomes of event not getting a prime number are 1, 4 and 6.
(ii) (a) The outcomes of event getting a number greater the 5 is 6.
(b) The outcomes of event not getting a number greater than 5 are 1, 2, 3, 4 and 5.

Q.3 Find the.
(a) Probability of the pointer stopping on D in (Question 1-(a))?
(b) Probability of getting an ace from a well shuffled deck of 52 playing cards?
(c) Probability of getting a red apple. (See figure below) Sol. (a) On spinning wheel, there are total 5 possible outcomes A, A, B, C, and D.
Here, the possibility of pointer stopping on D is 1.
Hence, the probability of the pointer stopping on D = ${1 \over 5}$
(b) A deck consists of total 52 cards and there are 4 ace cards in 1 deck of cards.
Hence, the probability of getting an ace from a deck = ${4 \over {52}} = {1 \over {13}}$
(c) In the figure, there are total 7 apples, out which there are 4 red apples.
Hence, the probability of getting a red apple = ${4 \over 7}$

Q.4 Numbers 1 to 10 are written on ten separate slips (one number on one slip), kept in a box and mixed well. One slip is chosen from the box without looking into it. What is the probability of .
(i) getting a number 6?
(ii) getting a number less than 6?
(iii) getting a number greater than 6?
(iv) getting a 1-digit number?
Sol. (i) There are total 10 slips in the box, out of which 6 is written only on 1 slip.
Hence, the probability of getting a number 6 = ${1 \over {10}}$
(ii) There are total 10 slips in the box, out of which there are 5 slips 1, 2, 3, 4 and 5 having number less than 6.
Hence, the probability of getting a number less than 6 = ${5 \over {10}} = {1 \over 2}$
(iii) There are total 10 slips in the box, out of which there are 4 slips 7, 8, 9 and 10 having number greater than 6.
Hence, the probability of getting a number greater than 6 = ${4 \over {10}} = {2 \over 5}$
(iv) There are total 10 slips in the box, out of which there are 9 slips 1, 2, 3, 4, 5, 6, 7, 8 and 9 having single digit number.
Hence, the probability of getting a single digit number = ${9 \over {10}}$

Q.5 If you have a spinning wheel with 3 green sectors, 1 blue sector and 1 red sector, what is the probability of getting a green sector? What is the probability of getting a non blue sector?
Sol. Here, total number of sectors = 3 + 1 + 1 = 5.
Now, there are 3 green sectors out of total 5 sectors.
Hence, the probability of getting a green sector = ${3 \over 5}$
Now, there will total 4 non blue sectors as we have 3 green sectors and 1 red sector out of total 5 sectors.
Hence, the probability of getting a non blue sector = ${4 \over 5}$

Q.6 Find the probabilities of the events given in Question 2.
Sol. On throwing a dice, there are total 6 possible outcomes which are 1, 2, 3, 4, 5, and 6.
(i) (a) There are 3 possible outcomes of event getting a prime number which are 2, 3 and 5.
Hence, probability of getting a prime number = ${3 \over 6} = {1 \over 2}$
(b) There are 3 possible outcomes of event not getting a prime number which are 1, 4 and 6.
Hence, probability of not getting a prime number = ${3 \over 6} = {1 \over 2}$
(ii) (a) There is only 1 possible outcome of event getting a number greater the 5 which is 6.
Hence, probability of getting a number greater than 5 = ${1 \over 6}$
(b) There are 5 possible outcomes of event not getting a number greater than 5 which are 1, 2, 3, 4 and 5.
Hence, probability of not getting a number greater than 5 = ${5 \over 6}$

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