CBSE Class 10 Maths Chapter 15 Probability NCERT Solutions

The fundamental relationship between the probability of an event and its complement is given by:

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

Using this, we can 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. Such an event is called a sure event or a certain event.

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

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

Equally likely outcomes mean that each outcome has the same chance of occurring.

(i) This is not an equally likely event. Whether the car starts depends on many factors like the car's condition, fuel, battery, etc. These factors are not necessarily balanced for both outcomes (starting vs. not starting).

(ii) 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) This is an equally likely event. In a true-false question, assuming the student has no prior knowledge, there are two options, and each has an equal chance of being chosen correctly or incorrectly.

(iv) This is generally considered an equally likely event. While biological factors can influence this, for the purpose of basic probability, the birth of a boy or a girl is typically treated as having equal probability.

Tossing a coin is considered a fair method because it has only two possible outcomes: heads or tails. In a fair coin toss, both outcomes are equally likely, meaning each has a 50% chance of occurring. Since there is no bias towards either outcome, it provides an unbiased way to make a decision between two options (e.g., which team gets possession).

The probability of any event, P(E), must satisfy the condition $0\; \backslash le\; P(E)\; \backslash le\; 1$. This means probability values must be between 0 and 1, inclusive.

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

(B) -1.5 is a negative number, which is less than 0. Therefore, it cannot be a probability of an event.

(C) 15% can be written as $\backslash frac\{15\}\{100\}\; =\; 0.15$, which is between 0 and 1 and is a valid probability.

(D) 0.7 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 $P(E)\; =\; 0.05$. To find the probability of 'not E', we rearrange the formula:

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

Substituting the given value:

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

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

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