The probability that a person who undergoes a bypass surgery will recover is 0.6 . the probability that of…

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
  1. 0.2762
  2. 0.1852
  3. 0.2074
  4. 0.7235

Solution

Probability of success, $p=0.6, q=0.4, n=6$ $\begin{aligned} \therefore \quad & \text { Random variable } \mathrm{X} \sim \mathrm{~B}(6,0.6) \\ & \text { Required probability } \\ & =\mathrm{p}(\mathrm{X}=3) \\ & ={ }^6 \mathrm{C}_3 \mathrm{p}^3 \mathrm{q}^3 \\ & =\frac{6 \times 5 \times 4 \times 3!}{3!\times 3!} \times(0.6)^3 \times(0.4)^3 \\ & =20 \times 0.216 \times 0.064 \\ & \approx 0.2762 \end{aligned}$

Asked in: MHT CET 2024 (11 May Shift 1)

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