CBSE Class 10 Mathematics Chapter 15 Probability NCERT Solutions

The fundamental relationship between the probability of an event and the probability of its complement is key here. Let P(E) be the probability of an event E, and P(E') be the probability of the event 'not E' (the complement of E).

The statement Probability of an event E + Probability of the event 'not E' = 1.

Now, let's complete the statements:

(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 always 1.

(v) The probability of an event is greater than or equal to 0 and less than or equal to 1. This means \(0 \le P(E) \le 1\).

Equally likely outcomes mean that each outcome has the same probability of occurring. Let's analyze each case:

(i) Starting a car: This is not an equally likely event. Whether the car starts or not depends on many factors like the car's condition, fuel, battery, etc. The probability of starting and not starting is not necessarily equal.

(ii) Shooting a basketball: This is not an equally likely event. The outcome depends heavily on the player's skill, practice, and the specific situation. Missing a shot might be more probable than making it, or vice versa, depending on the player.

(iii) Answering a true-false question: This is an equally likely event. Assuming the person does not know the answer and guesses randomly, there are two possibilities: right or wrong, each with a probability of 1/2.

(iv) A baby is born: This is generally considered an equally likely event. While biological factors can slightly influence the probability, for practical purposes in probability problems, the birth of a boy or a girl is treated as having equal likelihood (probability of 1/2 for each).

Tossing a coin is considered a fair method because it has only two possible outcomes: heads or tails. When a fair coin is tossed, both outcomes have an equal probability of occurring (each with a probability of 1/2). This means neither outcome is favored, making the result unpredictable and fair for deciding which team gets the ball.

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

(A) $\backslash frac\{2\}\{2\}$: This simplifies to 1, which is a valid probability (for a sure event).

(B) -1.5: This value is negative and less than 0. Probabilities cannot be negative.

(C) 15%: This can be written as $\backslash frac\{15\}\{100\}$ or 0.15. This value is between 0 and 1, so it is a valid probability.

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

Therefore, -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.

Substituting the given value into the formula:

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

To find P(not E), we subtract 0.05 from both sides of the equation:

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

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

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