MadeEasy Test Series: Probabilty - Probability

Question

The probability of a man hitting a target in one fire is 1/6. The number of times at least he must fire at the target in order that his chance of hitting the target at least once will exceed 2/5 will be ?

Comments

1 trial > p probability of success

?         >   p'

=p'/p

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Ans is 3 trials.

Refer here :- https://gateoverflow.in/289176/made-easy-test

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Answer 1

You can think of this as Bernoulli's experiment with $p = \dfrac{1}{6}$

In case of Bernoulli's experiment, expectation is $p$. That means in 1 trial you will get success p times.

1 trial -> p times

 ? trial -> 2/5 times

You can cross multiply, and get ans.

$? = \dfrac{2}{5p} = \dfrac{12}{5} = 3 $ trials.