Master probability in real-life scenarios with this CBSE Class 11 Applied Mathematics guide. Includes solved examples, MCQs, and NCERT-style practice sets.
Probability measures the likelihood of an event occurring in a random experiment. For a sample space S, the probability of an event E is the ratio of the number of favorable outcomes to the total number of equally likely outcomes. In real-life, this is used to predict outcomes in games, insurance, and quality control.
Step 1: Identify sample space S = {1, 2, 3, 4, 5, 6}, so n(S) = 6.
Step 2: Identify event E of getting an even number, E = {2, 4, 6}, so n(E) = 3.
Step 3: Calculate P(E) = 3/6 = 0.5.
Answer: 0.5
When dealing with two events A and B, the probability of either A or B occurring is given by the addition theorem. This is essential for real-life situations where events are not mutually exclusive, such as a student passing both Mathematics and Economics.
Step 1: Let A be drawing a King (4/52) and B be drawing a Heart (13/52).
Step 2: The intersection A ∩ B is the King of Hearts (1/52).
Step 3: P(A ∪ B) = 4/52 + 13/52 − 1/52 = 16/52 = 4/13.
Answer: 4/13
The probability of an event not occurring is the complement of the event occurring. This is highly useful in real-life risk assessment, where we calculate the probability of failure as 1 minus the probability of success.
Step 1: Probability of a bulb being defective is 0.05.
Step 2: The probability of the bulb being non-defective is P(E') = 1 − 0.05.
Step 3: P(E') = 0.95.
Answer: 0.95