# If an event cannot occur, then its probability is

a. 1

b. 3/4

c. 1/2

d. 0

**Solution:**

The probability of an event can be calculated by probability formula by simply dividing the favorable number of outcomes by the total number of possible outcomes.

1. Probability of an event will not be less than 0. It is because 0 is impossible.

2. Probability of an event will not be more than 1. It is because 1 is certain that it will happen.

An event which is certain to happen has a probability of occurrence of 1.

So the probability of non occurrence is 0

Probability of an impossible event is 0

Probability (non occurring event) = 0

Therefore, the probability is 0.

**✦ Try This: **If A and B are two independent events, the probability that both A and B occur is 1/8 and the probability that neither of them occurs is 3/8, The probability of the occurrence of A is a. 1/2, b. 1/3, c. 1/4, d. 1/5

Consider P(A) = x and P (B) = y

xy = 1/8

(1 - x) (1 - y) = 3/8

By further simplification

1 - x - y + xy = 3/8

Substituting the value of xy

1 - x - y + 1/8 = 3/8

1 - x - y = 3/8 - 1/8

1 - x - y = 2/8

1 - x - y = 1/4

x + y = 1 - 1/4 = 3/4

So x and y can take values 0.5 and 0.25

Therefore, the probability of occurrence of A is 1/2 and 1/4.

**☛ Also Check: **NCERT Solutions for Class 10 Maths Chapter 14

**NCERT Exemplar Class 10 Maths Exercise 13.1**** Problem 12**

## If an event cannot occur, then its probability is a. 1, b. 3/4, c. 1/2, d. 0

**Summary:**

The total number of outcomes of a random experiment is called an event. If an event cannot occur, then its probability is 0

**☛ Related Questions:**

- Which of the following cannot be the probability of an event a. 1/3, b. 0.1, c. 3%, d. 17/16
- An event is very unlikely to happen. Its probability is closest to a. 0.0001, b. 0.001, c. 0.01, d. . . . .
- If the probability of an event is p, the probability of its complementary event will be a. p - 1, b. . . . .

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