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JEE Main 202125 FebruaryMorning Shift
Exam
JEE Main
Year
2021
Date
25 February
Shift
Morning Shift
Subject
Mathematics
Chapter
Probability

JEE Main 2021 · 25 February · Morning Shift · Mathematics · Probability

When a missile is fired from a ship, the probability that it is...

When a missile is fired from a ship, the probability that it is intercepted is 13\dfrac{1}{3} and the probability that the missile hits the target, given that it is not intercepted, is 34.\dfrac{3}{4} . If three missiles are fired independently from the ship, then the probability that all three hit the target, is:

Options

  1. A38\dfrac{3}{8}
  2. B127\dfrac{1}{27}
  3. C18\dfrac{1}{8}
  4. D34\dfrac{3}{4}

Correct answer

C. 18\dfrac{1}{8}

Step-by-step solution

Probability of not getting intercepted =23= \dfrac{2}{3}

Probability of missile hitting target =34= \dfrac{3}{4}

∴∴ Probability that all 33 hit the target =(23×34)3=18= {\left(\dfrac{2}{3} \times \dfrac{3}{4}\right)}^{3} = \dfrac{1}{8}

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