**NCERT Class 10 Maths Lab Manual – Probability**

**Objective**

To set the idea of probability of an event through a double colour cards experiment.

**Prerequisite Knowledge**

- Sample space and event.
- Total number of possible outcomes.
- Favourable outcomes.
- Probability of an event = \(\frac{No.offavourable\quad outcomes}{Total\quad no.of\quad Possible\quad outcomes}\).

**Material Required**

A cardboard of size 18 cm x 18 cm, two colour papers say pink and blue, pair of dice, empty box, pair of scissors, sketch pens, fevicol, etc.

**Procedure**

- Paste different colour papers, blue and pink on both sides of the board, (such that pink on one side and blue on another side)
- Divide the board into 36 small squared cards.
- Write all 36 possible outcomes obtained by throwing two dice, e.g., for the outcome (4,5), write 4 on the blue side and 5 on pink side.
- Cut and put all the cards into a box.
- Now take out each card one by one without replacement and write the observation in appropriate column.

**Observation**

- Total number of possible outcomes =
- Total number of favourable outcomes of sum 2 =
- Total number of favourable outcomes of sum 3 =
- Total number of favourable outcomes of sum 4 =
- Total number of favourable outcomes of sum 5=
- Total number of favourable outcomes of sum 6 =
- Total number of favourable outcomes of sum 7 =
- Total number of favourable outcomes of sum 8 =
- Total number of favourable outcomes of sum 9 =
- Total number of favourable outcomes of sum 10 =
- Total number of favourable outcomes of sum 11 =
- Total number of favourable outcomes of sum 12 =
- Total number of favourable outcomes (sum ≥11) =
- Total number of favourable outcomes (sum >12) =
- Total number of favourable outcomes (sum < 7) =

Using formula calculate the required Probability of each event.

Sample space (when two dice are thrown)

**Example:** Number of favourable outcomes of sum of numbers 2=1

Total outcomes = 36

∴ Probability of sum of numbers is 2 = \(\frac { 1 }{ 36 }\)

Similarly find other probabilities for different outcomes of sum.

**Result**

Probability of an event = \(\frac{No.offavourable\quad outcomes}{Total\quad no.of\quad Possible\quad outcomes}\)

**Learning Outcome**

Concept of finding the probability of an event is clear through this activity.

**Activity Time**

- What is the probability of getting the sum of two numbers more than 17?
- Write the sample space, when a coin is tossed 3 times.
- A game of chance consists of spinning an arrow which comes to rest pointing at one of the numbers 1, 2, 3, 4, 5, 6, 7, 8 as shown in the fig. and these are equally likely outcomes. What is the probability that it will point at

- 8?
- an odd number ?
- a number greater than 2 ?
- a number less than 9 ?
- a numberless than 1 ?

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**Viva Voce**

**Question 1.**

What is probability ?

**Answer:**

The possibility (or possibilites) of occuringornotoccuringof an eventis called probability.

Probability or an event = \(\frac{No.of favourable\quad outcomes}{Total\quad no.of\quad Possible\quad outcomes}\)

**Question 2.**

What is a sample space ?

**Answer:**

It is the set of all possible outcomes of a random experiment.

**Question 3.**

What is the probability of an impossible event, sure event respectively ?

**Answer:**

Zero, one.

**Question 4.**

A dice is thrown twice. How many elements are possible in sample space ?

**Answer:**

36.

**Question 5.**

If P(E) = 0.05, what is the probability of ‘not E’ ?

**Answer:**

0.95.

**Question 6.**

What is the sum of the probabilities of all the elementary events of an experiment ?

**Answer:**

One

**Question 7.**

A bag contains 3 red and 5 black balls. A ball is drawn at random. What is the probability that the ball is red ?

**Answer:**

\(\frac { 3 }{ 8 }\)

**Question 8.**

A die is thrown once. What is the probability of getting a prime number ?

**Answer:**

\(\frac { 3 }{ 6 } =\frac { 1 }{ 2 }\)

**Question 9.**

One card is drawn from a well shuffled deck of 52 cards. What is the probability of a king of red colour ?

**Answer:**

\(\frac { 2 }{ 52 } =\frac { 1 }{ 26 }\)

**Multiple Choice Questions**

**Question 1.**

A die is thrown twice. What is the probability that 5 will not come up either ?

(Hint: meaning is 5 is not coming in first throw as well as in second throw).

(a) \(\frac { 25 }{ 36 }\)

(b) \(\frac { 17 }{ 36 }\)

(c) \(\frac { 15 }{ 36 }\)

(d) None of these

**Question 2.**

17 cards numbered 1, 2, 3, … 17 are put in a box and mixed. One person draws a cards. Find the probability that the number on the card is prime.

(a) \(\frac { 15 }{ 17 }\)

(b) \(\frac { 7 }{ 17 }\)

(c) \(\frac { 8 }{ 17 }\)

(d) \(\frac { 9 }{ 17 }\)

**Question 3.**

The king, queen and jack of clubs are removed from a pack of 52 cards and then well shuffled. One card is selected from the remaining cards. Find the probability of getting ‘The ’10’ of heart’.

(a) \(\frac { 9 }{ 49 }\)

(b) \(\frac { 10 }{ 49 }\)

(c) \(\frac { 1 }{ 49 }\)

(d) None of these

**Question 4.**

A bag contains 5 red and some blue balls. If the probability of drawing a blue ball is double that of a red ball, find the number of blue balls in the bag.

(a) 10

(b) 5

(c) 20

(d) none of these

**Question 5.**

A coin is tossed three time what is the probability of getting the same result in each trial ?

(a) \(\frac { 1 }{ 4 }\)

(b) \(\frac { 1 }{ 8 }\)

(c) \(\frac { 3 }{ 8 }\)

(d) None of these

(**Hint:** TTT or HHH, ∴\(\frac { 2 }{ 8 } =\frac { 1 }{ 4 }\))

**Question 6.**

If P(E) = 0.65 then P is (\(\overset { – }{ E }\))

(a) 0.15

(b) 0.30

(c) 0.35

(d) none of these

**Question 7.**

Which of the following cann’t be the event of probability ?

(a) \(\frac { 2 }{ 3 }\)

(b) -1.5

(c) 15%

(d) 0.7

**Question 8.**

If probability of ‘not E’ is 0.98, then P(E) is

(a) 0.5

(b) 0.02

(c) 0.005

(d) 1

**Question 9.**

In a non-leap year there are 365 days i.e., 52 weeks and 1 day. Find the probability of getting 53 Sunday.

(a) \(\frac { 1 }{ 7 }\)

(b) \(\frac { 2 }{ 7 }\)

(c) \(\frac { 3 }{ 7 }\)

(d) None of these

**Question 10.**

Find the probabilitty of getting 53 Mondays in a leap year.

(a) \(\frac { 1 }{ 7 }\)

(b) \(\frac { 2 }{ 7 }\)

(c) 1

(d) none of these

**Answers**

- (a)
- (b)
- (c)
- (a)
- (a)
- (c)
- (b)
- (b)
- (a)
- (b)

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