CBSE Class 10 Mathematics Chapter 15 Probability NCERT Solutions

The statements are completed based on the fundamental axioms of probability:

(i) The probability of an event that cannot happen is 0. Such an event is called an impossible event.

(ii) The probability of an event that is certain to happen is 1.

(iii) Such an event is called a sure event or a certain event.

(iv) The sum of the probabilities of all the elementary events of an experiment is 1.

(v) The probability of an event is greater than or equal to 0 and less than or equal to 1.

Outcomes are considered equally likely if each outcome has the same probability of occurring. Let's analyze each case:

(i) A driver attempts to start a car. The car starts or does not start.

This is not an equally likely event. Whether the car starts depends on various factors like the car's condition, fuel, battery, etc. The probability of the car starting is not necessarily equal to the probability of it not starting.

(ii) A player attempts to shoot a basketball. She/he shoots or misses the shot.

This is not an equally likely event. The outcome depends heavily on the player's skill, practice, and the specific situation. A skilled player might have a higher probability of making the shot than missing it.

(iii) A trial is made to answer a true-false question. The answer is right or wrong.

This is an equally likely event. Assuming the student has no prior knowledge and is guessing randomly, there are two possible outcomes (right or wrong), and each has an equal chance of occurring.

(iv) A baby is born. It is a boy or a girl.

This is generally considered an equally likely event in basic probability contexts. While there might be slight statistical variations in birth rates, for practical purposes and theoretical understanding, the birth of a boy and the birth of a girl are treated as having equal probabilities.

Tossing a coin is considered a fair method because it has only two possible outcomes: heads or tails. For a fair coin, these two outcomes are equally likely, meaning each has a probability of 1/2. Since both outcomes have an equal chance of occurring, neither outcome is favored, making it a random and unbiased way to make a decision.

The probability of any event, P(E), must satisfy the condition $0 \le P(E) \le 1$. Let's examine each option:

(A) $\backslash frac\{2\}\{2\}$ = 1. This is a valid probability.

(B) -1.5. This value is negative, which is outside the valid range [0, 1]. Therefore, it cannot be the probability of an event.

(C) 15%. Converting this to a decimal gives 0.15, which is within the valid range [0, 1].

(D) 0.7. This value is between 0 and 1, so it is a valid probability.

Thus, -1.5 cannot be the probability of an event.

The correct option is (B).

We know that for any event E, the sum of the probability of the event occurring and the probability of the event not occurring is always 1. This can be written as:

$$P(E)\; +\; P(\backslash text\{not\; \}\; E)\; =\; 1$$

We are given that $P(E)\; =\; 0.05$. We need to find $P(\backslash text\{not\; \}\; E)$.

Substituting the given value into the formula:

$$0.05\; +\; P(\backslash text\{not\; \}\; E)\; =\; 1$$

To find $P(\backslash text\{not\; \}\; E)$, we subtract 0.05 from both sides of the equation:

$$P(\backslash text\{not\; \}\; E)\; =\; 1\; -\; 0.05$$

$$P(\backslash text\{not\; \}\; E)\; =\; 0.95$$

Therefore, the probability of 'not E' is 0.95.