Three persons A, B and C, fire at a target in turn, starting with A. Their probability of hitting the target are 0.4, 0.3 and 0.2 respectively. The probability of two hits is
Probability is the measure of the likelihood of an event occurring. It ranges from 0 (impossible event) to 1 (certain event). The probability of an event is calculated as the ratio of favorable outcomes to total possible outcomes. It is widely used in statistics, decision-making, and real-world predictions.
Class 12 Maths Probability is taught in Chapter 13 for the CBSE Exam 2024-25. It covers essential topics like random experiments sample space independent and dependent events mutually exclusive and non-mutually exclusive events Bayes’ theorem and conditional probability. Understanding these concepts is crucial for solving real-life problems and performing well in competitive exams.
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Given:
P(A hits) = 0.4
P(B hits) = 0.3
P(C hits) = 0.2
To find the probability of exactly two hits, we consider the cases where exactly two of A, B, and C hit the target:
1. A and B hit, C misses:
P(A ∩ B ∩ C’) = (0.4) × (0.3) × (1 – 0.2)
= 0.4 × 0.3 × 0.8 = 0.096
2. A and C hit, B misses:
P(A ∩ B’ ∩ C) = (0.4) × (1 – 0.3) × (0.2)
= 0.4 × 0.7 × 0.2 = 0.056
3. B and C hit, A misses:
P(A’ ∩ B ∩ C) = (1 – 0.4) × (0.3) × (0.2)
= 0.6 × 0.3 × 0.2 = 0.036
Total probability of exactly two hits:
P = 0.096 + 0.056 + 0.036 = 0.188
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