# Probability

## NCERT Exercise 15.1

### Part 1

Question 1: Which of the following experiments have equally likely outcomes? Explain.

- A driver attempts to start a car. The car starts or does not start.
- A player attempts to shoot a basketball. She/he shoots or misses the shot.
- A trial is made to answer a true-false question. The answer is right or wrong.
- A baby is born. It is a boy or a girl.

**Answer:** All events have two possible outcomes so both outcomes are equally likely.

Question 2: Complete the following statements:

- Probability of an event E + Probability of the event ‘not E’ = …………
**Answer:**1 - The probability of an event that cannot happen is ..... Such an event is called......
**Answer:**0 . Impossible Event - The probability of an event that is certain to happen is ..... Such an event is called ......
**Answer:**1, Sure Event - The sum of the probabilities of all the elementary events of an experiment is
**Answer:**1 - The probability of an event is greater than or equal to and less than or equal to.
**Answer:**`0≤P(E)≤1`

Question 3: Why is tossing a coin considered to be a fair way of deciding which team should get the ball at the beginning of a football game?

**Answer:** Because of equal chance of both outcomes

Question 4: Which of the following cannot be the probability of an event?

(A) 2/3 (B) –1.5 (C) 15% (D) 0.7

**Answer:** B cannot be a probability as it has negative value

Question 5: If P(E) = 0.05, what is the probability of ‘not E’?

**Solution:** P(E) = 0.05

`=(5)/(100)=(1)/(20)`

Or, P(not E)

`=1-(1)/(20)=(19)/(20)`

Question 6: A bag contains lemon flavoured candies only. Malini takes out one candy without looking into the bag. What is the probability that she takes out

(i) an orange flavoured candy?

**Solution:** Zero

(ii) a lemon flavoured candy?

**Solution:** 1

Question 7: It is given that in a group of 3 students, the probability of 2 students not having the same birthday is 0.992. What is the probability that the 2 students have the same birthday?

**Solution:** `1 – 0.992 = 0.008`

Question 8: A bag contains 3 red balls and 5 black balls. A ball is drawn at random from the bag. What is the probability that the ball drawn is

**Solution:** Total number of outcomes `= 3 + 5 = 8`

Number of favourable outcomes = 3

Hence;

P(Red) `=3/8`

(ii) not red?

**Solution:**

P(not Red) `=1-3/8=5/8`

Question 9: A box contains 5 red marbles, 8 white marbles and 4 green marbles. One marble is taken out of the box at random. What is the probability that the marble taken out will be

**Solution:** Total number of outcomes = 5 + 8 + 4 = 17

Number of red marbles = 5

Number of white marbles = 8

Number of green marbles = 4

(i) Red?

**Solution:** Probability of red marbles;

`P(R)=(5)/(17)`

(ii) White?

**Solution:** Probability of white marbles;

`P(W)=(8)/(17)`

(iii) Not green?

**Solution:** Probability of green marbles;

`P(G)=(4)/(17)`

Or, P(not G) `=1-(4)/(17)=(13)/(17)`

Question 10: A piggy bank contains hundred 50p coins, fifty Re 1 coins, twenty Rs 2 coins and ten Rs 5 coins. If it is equally likely that one of the coins will fall out when the bank is turned upside down, what is the probability that the coin

(i) will be a 50 p coin?

**Solution:** Total number of events = 100 + 50 + 20 + 10 = 180

Number of 50 p coins = 50

P(50 p coins) `=(50)/(180)=(8)/(18)`

(ii) Will not be a Rs. 5 coin?

**Solution:** Number of Rs. 5 coins = 10

P(Rs. 5 coins) `=(10)/(180)=(1)/(18)`

Or, P(not Rs. 5) `=1-(1)/(18)=(17)/(18)`

Question 11: Gopi buys a fish from a shop for his aquarium. The shopkeeper takes out one fish at random from a tank containing 5 male fish and 8 female fish. What is the probability that the fish taken out is a male fish?

**Solution:** Total number of events = 5 + 8 = 13

Number of male fish = 5

P(male fish) `=(5)/(13)`

Question 12: 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, and these are equally likely outcomes. What is the probability that it will point at

(i) 8 ?

**Solution:** Total number of events = 8

Number of 8s = 1

`P(8)=1/8`

(ii) an odd number?

**Solution:** Number of odd numbers = 4

P(Odd number) `=4/8=1/2`

(iii) a number greater than 2?

**Solution:** Number of numbers greater than 2 = 6

`P(>2)=6/8=3/4`

(iv) a number less than 9?

**Solution:** 1 (since all numbers are less than 9)

Question 13: A die is thrown once. Find the probability of getting

(i) a prime number

**Solution:** Total number of events = 6

Number of prime numbers = 3

P(Prime numbers) `=3/6=1/2`

(ii) a number lying between 2 and 6

**Solution:** Number of numbers between 2 and 6 = 3

P(between 2 and 6) `=3/6=1/2`

(iii) an odd number.

**Solution:** Number of odd numbers = 3

P(Odd numbers) `=3/6=1/2`