Master the Concept of Probability for CBSE Class 11 Applied Mathematics with comprehensive theory, solved examples, and practice exercises.
Probability measures the likelihood of an event occurring, defined as the ratio of favorable outcomes to the total number of equally likely outcomes in a sample space. A sample space S is the set of all possible outcomes of a random experiment. For an event E ⊂ S, the probability P(E) always lies in the interval [0, 1].
Step 1: Identify sample space S = {1, 2, 3, 4, 5, 6}, so n(S) = 6.
Step 2: Let E be the event 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
The probability of an impossible event is 0, and the probability of a sure event is 1. For any two events A and B, the probability of the union is given by the Addition Theorem. This theorem accounts for the overlap between events to avoid double counting.
Step 1: Given P(A) = 0.4, P(B) = 0.3, and P(A ∩ B) = 0.1.
Step 2: Apply P(A ∪ B) = 0.4 + 0.3 − 0.1.
Step 3: Calculate 0.7 − 0.1 = 0.6.
Answer: 0.6
The complement of an event E, denoted by E' or Eᶜ, represents the event that E does not occur. The sum of the probability of an event and its complement is always 1. This property is useful for calculating probabilities of 'at least one' type problems.
Step 1: Given P(E) = 0.25.
Step 2: Use the formula P(Eᶜ) = 1 − 0.25.
Step 3: Calculate 1 − 0.25 = 0.75.
Answer: 0.75