Aspire Faculty ID #11639 · Topic: NIMCET 2024 · Just now
NIMCET 2024

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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