**Data Handling**

**Question 1.****List the outcomes you can see in these experiments.(a)** Spinning a wheel,

**(b)**Tossing two coins together.

**Solution:****(a)** List of outcomes of spinning the given wheel are A, B, C and D.**(b)** When two coins are tossed together, the possible outcomes of the experiment are HH, HT, TH and TT.

**Question 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.

**Solution:****(i)** In a throw of die, list of the outcomes of an event of getting**(a)** a prime number are 2, 3 and 5.**(b)** not a prime number are 1, 4 and 6. .

**(ii)** In a throw of die, list of the outcomes of an event of getting**(a)** a number greater than 5 is 6.**(b)** a number not greater than 5 are 1, 2, 3 and 4.

**Question 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 adjoining figure).

**Solution:****(a)** Out of 5 sectors, the pointer can stop dt any of sectors in 5 ways.

∴ Total number of elementary events = 5. There is only one ‘D’ on the spinning wheel.

∴ Favourable number of outcomes = 1

∴ Required probability =

**(b)** Out of 52 cards, one card can be drawn in 52 ways.

∴ Total number of outcomes = 52

There are 4 aces in a pack of 52 cards, out of which one ace can be drawn in 4 ways.

∴ Favourable number of cases = 4

So, the required probability =

**(c)** Out of 7 apples, one apple can be drawn in 7 ways.

∴ Total number of outcomes = 7

There are 4 red apples, in a bag of 7 apples, out of which 1 red apple can be drawn in 4 ways.

∴ Favourable number of case = 4

So, the required probability =

**Question 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?

**Solution:**

Out of 10 slips, 1 slip can be drawn in 10 ways. So, the total number of outcomes = 10**(i)** An event of getting a number 6, i. e., if we obtain a slip having number 6 as an outcome.

So, favourable number of outcomes = 1

∴ Required probability =

**(ii)** An event of getting a number less than 6, i. e., if we obtain a slip having any of numbers 1, 2, 3, 4, 5 as an outcome.

So, favourable number of cases = 5

∴ Required probability =

**(iii)** An event of getting a number greater than 6, i.e., if we obtain a slip having any of numbers 7, 8, 9, 10 as an outcome.

So, favourable number of cases = 4

∴ Required probability =

**(iv)** An event of getting a one-digit number, i.e., if we obtain a slip having any of numbers 1, 2, 3, 4, 5, 6, 7, 8, 9 as an outcome.

So, favourable number of cases = 9

∴ Required probability =

**Question 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?**

**Solution:**

Out of 5 sectors, the pointer can stop at any of sectors in 5 ways.

∴ Total number of outcomes = 5

There are 3 green sectors in the spinning wheel, out of which one can be obtained in 3 ways.

∴ Favourable number of outcomes = 3

So, the required probability =

Further, there are 4 non-blue sectors in the spinning wheel, out of which one can be obtained in 4 ways.

So, the required probability =

**Question 6.****Find the probabilities of the events given in Question 2.**

**Solution:**

In a single throw of a die, we can get any one of the six numbers 1, 2, 6 marked on its six faces.

Therefore, the total number of outcomes = 6

**(i)** Let A denote the event “getting a prime number”. Clearly, event A occurs if we obtain 2, 3, 5 as an outcome.

∴ Favourable number of outcomes = 3

Hence,

**(ii)** Let A denote the event “not getting a prime number”. Clearly, event A occurs if we obtain 1, 4, 6 as an outcome.

∴ Favourable number of outcomes = 3

Hence,

**(iii)** The event “getting a number greater than 5” will occur if we obtain the number 6.

∴ Favourable number of outcomes = 1

Hence, required probability =

**(iv)** The event “getting a number not greater than 5” will occur if we obtain one of the numbers 1, 2, 3, 4, 5.

∴ Favourable number of outcomes = 5

Hence, required probability =