The probability that a bomb dropped from a plane strikes the target is 1-5- The probability that out of 6 bombs dropped atleast 2 bombs strike the target

The correct option is A 0.345 The required probability is ∑ ^6_k=2 ^6C_k(p)^k(1 p)^6 k where p=1/5 Upon expanding we get #160;1/5^6[ ^6C_24^ ...

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Standard X

Mathematics

Probability

The probabili...

Question

The probability that a bomb dropped from a plane strikes the target is $\frac{1}{5}$ . The probability that out of $6$ bombs dropped atleast $2$ bombs strike the target

0.345

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Solution

The correct option is A $0.345$
The required probability is
$\sum_{k = 2}^{6}^{6} C_{k} (p)^{k} (1 - p)^{6 - k}$ where $p = \frac{1}{5}$
Upon expanding we get
$\frac{1}{5^{6}} [^{6} C_{2} 4^{4} +^{6} C_{3} 4^{3} +^{6} C_{4} 4^{2} +^{6} C_{5} 4^{1} +^{6} C_{6} 4^{0}]$
$= \frac{1}{5^{6}} [15 (256) + 20 (64) + 15 (16) + 6 (4) + 1]$
$= \frac{5385}{5^{6}}$
$= 0.345$

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The probability that a bomb dropped from a plane strikes the target is 15. The probability that out of 6 bombs dropped atleast 2 bombs strike the target

The correct option is A 0.345The required probability is∑6k=26Ck(p)k(1−p)6−k where p=15Upon expanding we get156[6C244+6C343+6C442+6C541+6C640]=156[15(256)+20(64)+15(16)+6(4)+1]=538556=0.345

The probability that a bomb dropped from a plane strikes the target is $\frac{1}{5}$ . The probability that out of $6$ bombs dropped atleast $2$ bombs strike the target