JEE Advanced · 2020 · 27 Sep 2020 · Paper 2 · Probability XII

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The probability that a missile hits a target successfully is 0.75. In order to destroy the target completely, at least three successful hits are required. Then the minimum number of missiles that have to be fired so that the probability of completely destroying the target is NOT less than 0.95, is ____

Answer: 6

Solution

Let

P (r)

be the probability of

r

successes in

n

trials:

P (r) =^{n} C_{r} (\frac{3}{4})^{r} (\frac{1}{4})^{n - r}

. We need at least 3 successes, so the probability is

1 - (P (0) + P (1) + P (2)) \geq 0.95

. This gives

1 - (\frac{1}{4})^{n} -^{n} C_{1} (\frac{3}{4}) (\frac{1}{4})^{n - 1} -^{n} C_{2} (\frac{3}{4})^{2} (\frac{1}{4})^{n - 2} \geq 0.95

. Simplifying:

9 n^{2} - 3 n + 2 \leq \frac{4 ^{n}}{10}

. For

n = 5

212 \neq \leq 102.4

(false). For

n = 6

308 \leq 409.6

(true). Therefore, the minimum value is 6.

JEE Advanced · 2020 · 27 Sep 2020 · Paper 2 · Integer answer

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JEE Advanced · 2020 · 27 Sep 2020 · Paper 2 · Probability XII

Solution

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