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Study Stuff for MCA Examinations - NIMCET
Study Stuff for MCA Examinations - NIMCET
Previous Year Question (PYQs)
A critical orthopedic surgery is performed on 3 patients. The probability of recovering
a patient is 0.6. Then the probability that after surgery, exactly two of them will recover
is
Solution
Given:
- Number of patients (n): 3
- Probability of recovery (p): 0.6
- Probability of failure (q): 0.4
- We are asked to find: Probability that exactly 2 out of 3 patients will recover.
Solution: We will use the Binomial Probability Formula to solve this.
Step 1: Binomial Probability Formula:
The formula is:
$$ P(X = r) = \binom{n}{r} p^r (1 - p)^{n - r} $$
Where:
\( n = 3 \), \( r = 2 \), \( p = 0.6 \), \( 1 - p = 0.4 \)
Step 2: Calculate the binomial coefficient \( \binom{3}{2} \):
$$ \binom{3}{2} = \frac{3!}{2!(3-2)!} = 3 $$Step 3: Substitute values into the formula:
$$ P(X = 2) = 3 \times (0.6)^2 \times (0.4)^1 = 3 \times 0.36 \times 0.4 = 0.432 $$✅ Final Answer: 0.432
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