**GSEB Solutions for Class 10 mathematics – Probability (English Medium)**

### Exercise-16

**Question 1:**

15 defective ballpens are accidentally mixed with 135 good ones. It is not possible to just look at a ballpen and say whether it is defective or not. One ballpen is picked up at random from it. Find the probability that the ballpen selected is a good one.

**Solution :**

**Question 2:**

A box contains 5 green, 8 yellow and 7 brown balls. One ball is taken out from a box at random. What is the probability that the ball taken out is (i) yellow ? (ii) brown ? (iii) neither green nor brown ? (iv) not brown ?

**Solution :**

**Question 3:**

A bag contains orange flavoured candies only. Rahi takes out one candy without looking into the bag. What is the probability that she takes out (i) the orange flavoured candy ? (ii) a lemon flavoured candy ?

**Solution :**

**Question 4:**

A box contain 100 cards marked with numbers 1 to 100. If one card is drawn from the box, find the probability that it bears (i) single digit number, (ii) two-digit numbers (iii) three-digit number (iv) a number divisible by 8 (v) a multiple of 9, (vi) a multiple of 5.

**Solution :**

**Question 5:**

A carton consist of 100 trousers of which 73 are good, 12 have minor defects and 15 have major defects. Kanu, a trader, will only accept the trousers which are good, but Radha, another trader, will only reject the trousers which have major defects. One trouser is drawn at random from the carton. What is the probability that,

(i) it is acceptable to Kanu ? (ii) it is acceptable to Radha ?

**Solution :**

**Question 6:**

Marks obtained by 50 students from 100 are as follows

Find the probability that a student get marks :

- below 34,
- between 71-90
- more than 70
- less than or equal to 50

**Solution :**

**Question 7:**

Two fair dice are rolled simultaneously. Find the probability of the following events :

- A : getting the same number on both dice.
- B : the sum of the integers on two dice is more than 4 but less than 8.
- C : the product of numbers on two dice is divisible by 2.
- D : the sum of numbers on two dice is greater than 12.

**Solution :**

**Question 8:**

A coin is tossed three times. Find the probability of the following events :

- A : getting at least two heads,
- B : getting exactly two heads,
- C : getting at most one head,
- D : getting more heads than tails.

**Solution :**

**Question 9:**

A game of chance consists of spinning an arrow which comes to rest pointing numbers 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12 (see figure 16.1) and there are outcomes. What is the probability that it will point at

- 7?
- a number greater than 9 ?
- an odd number ?
- an even number ?
- a number less than 5 ?

**Solution :**

**Question 10:**

Select a proper option (a), (b), (c) or (d) from given options and write in the box given on the right so that the statement becomes correct :

**Question 10(1):**

**Solution :**

**Question 10(2):**

**Solution :**

d. 1

An event which always occurs is known as a certain event.

∴ The probability of a certain event is 1.

**Question 10(3):**

**Solution :**

a. 0

An event which never occurs is known as an impossible event.

∴ The probability of an impossible event is 0.

**Question 10(4):**

**Solution :**

**Question 10(5):**

**Solution :**

**Question 10(6):**

**Solution :**

**Question 10(7):**

**Solution :**

**Question 10(8):**

**Solution :**

c. 0

The paper in my hand is of 100 marks. So, to get 101 marks out of 100 in this paper is an impossible event. The probability of an impossible event is 0.

**Question 10(9):**

**Solution :**

c. 0

The event ‘The Sun rises in the West’ is an impossible event and thus its probability is 0.

**Question 10(10):**

**Solution :**

c. 1

If A_{1}, A_{2}, A_{3}, ……….., A_{k} are all the elementary events of an experiment, then P(A_{1}) + P(A_{2}) + P(A_{3}) ……………. + P(A_{k}) = 1.

XYZ says

Nice solution.

Thanks for it.

Monika says

Thank you so much it is very helpful for students.