MHT CET · Maths · Probability
The probability that a person who undergoes a bypass surgery will recover is 0.6 . the probability that of the six patients who undergo similar operations, half of them will recover is
- A 0.2762
- B 0.1852
- C 0.2074
- D 0.7235
Answer & Solution
Correct Answer
(A) 0.2762
Step-by-step Solution
Detailed explanation
Probability of success, \(p=0.6, q=0.4, n=6\)
\(\begin{aligned}
\therefore \quad & \text { Random variable } \mathrm{X} \sim \mathrm{~B}(6,0.6) \\
& \text { Required probability } \\
& =\mathrm{p}(\mathrm{X}=3) \\
& ={ }^6 \mathrm{C}_3 \mathrm{p}^3 \mathrm{q}^3 \\
& =\frac{6 \times 5 \times 4 \times 3!}{3!\times 3!} \times(0.6)^3 \times(0.4)^3 \\
& =20 \times 0.216 \times 0.064 \\
& \approx 0.2762
\end{aligned}\)
\(\begin{aligned}
\therefore \quad & \text { Random variable } \mathrm{X} \sim \mathrm{~B}(6,0.6) \\
& \text { Required probability } \\
& =\mathrm{p}(\mathrm{X}=3) \\
& ={ }^6 \mathrm{C}_3 \mathrm{p}^3 \mathrm{q}^3 \\
& =\frac{6 \times 5 \times 4 \times 3!}{3!\times 3!} \times(0.6)^3 \times(0.4)^3 \\
& =20 \times 0.216 \times 0.064 \\
& \approx 0.2762
\end{aligned}\)
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