Probability Video Lecture | Mathematics (Maths) Class 10

Ans. Probability is a measure of the likelihood of an event occurring, expressed as a number between 0 and 1. To calculate the probability of an event, you use the formula: \[ P(E) = \frac{\text{Number of favorable outcomes}}{\text{Total number of possible outcomes}} \] For example, if you have a six-sided die and want to find the probability of rolling a 4, there is 1 favorable outcome (rolling a 4) out of 6 possible outcomes, so \( P(4) = \frac{1}{6} \).

Ans. There are three main types of probability: 1. <b>Theoretical Probability</b>: Based on reasoning or the nature of the event. For example, the probability of flipping heads in a fair coin is \( \frac{1}{2} \). 2. <b>Experimental Probability</b>: Based on the results of an experiment or trial. For instance, if you flip a coin 100 times and get heads 45 times, the experimental probability of heads is \( \frac{45}{100} = 0.45 \). 3. <b>Subjective Probability</b>: Based on personal judgment or experience rather than exact calculations.

Ans. The probability of compound events can be found using the rules of addition and multiplication. For two independent events A and B: - If you want to find the probability of either A or B occurring (union), use: \[ P(A \cup B) = P(A) + P(B) - P(A \cap B) \] - If you want to find the probability of both A and B occurring (intersection), use: \[ P(A \cap B) = P(A) \times P(B) \] For example, if the probability of rain is \( \frac{1}{4} \) and the probability of a traffic jam is \( \frac{1}{3} \), then: \[ P(\text{Rain or Traffic Jam}) = P(\text{Rain}) + P(\text{Traffic Jam}) - P(\text{Rain and Traffic Jam}) \]

Ans. The sample space is the set of all possible outcomes of a probability experiment. It is crucial because it provides a complete picture of all events that can occur, allowing us to accurately calculate probabilities. For instance, if you flip a coin, the sample space is {Heads, Tails}. Understanding the sample space helps to identify favorable outcomes and prevents errors in probability calculations.

Ans. Complementary events are pairs of outcomes that together cover all possible outcomes of an event. For an event A, the complementary event (denoted as A') is the event that A does not occur. The probability of complementary events is given by: \[ P(A') = 1 - P(A) \] For example, if the probability of it raining tomorrow (event A) is \( \frac{1}{4} \), then the probability of it not raining (event A') is: \[ P(A') = 1 - \frac{1}{4} = \frac{3}{4} \]