Assume that the probability that a bomb dropped from an aeroplane… - Vidyadip

Question

Assume that the probability that a bomb dropped from an aeroplane will strike a certain target is 0.2. If 6 bombs are dropped, find the probability that.

exactly 2 will strike the target.
at least 2 will strike the target.

✓

Answer

probabilty that bomb strikes a target p = 0.2
Probability that a bomb misses the target = 0.8
n = 6
let X = number of bombs that strike the target
P(X = 2) = exactly 2 bombs strike the target
$=\text{ }^6\text{C}_2\big(\frac{2}{10}\big)^2\times\big(\frac{8}{10}\big)^4=15\times\frac{16384}{10^6}=0.24576$
$\text{P(X}\geq2)=$ at least 2 bombs strike the target
$=1-\text{P(X}<2)$
$=1-\big[\text{P(X}=0)+\text{P(X=1})\big]$
$=1-\big[\text{ }^6\text{C}_0\big(\frac{2}{10}\big)^0\times\big(\frac{8}{10}\big)^6+\text{ }^6\text{C}_1\big(\frac{2}{10}\big)^1\times\big(\frac{8}{10}\big)^6\big]$
$=1-\big[0.0.262144+0.393216\big]=1-0.65536$
$=0.34464$

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "4 Marks" from Probability→Probability — all question types→Maths STD 12 Science question papers→Gujarat Board STD 12 Science question papers→Gujarat Board question paper generator→

Similar questions

$\int\limits^{\frac{\pi}{4}}_{-\frac{\pi}{4}}\log(\sin\text{x}+\cos\text{x})\text{dx}$

A library has to accommodate two different types of books on a shelf. The books are 6 cm and 4 cm thick and weigh 1kg and $1\frac{1}{2}$ kg each respectively. The shelf is 96 cm long and at most can support a weight of 21kg. How should the shelf be filled with the books of two types in order to include the greatest number of books? Make it as an LPP and solve it graphically.

Find the area of the region bounded by the curve y = x - 1 and (y - 1)² = 4(x + 1).

Write the points where f(x) = |log_e x| is not differentiable.

Find the area of the figure bounded by the curves y = |x - 1| and y = 3 - |x|.

find the area of the region enclosed by the parbola x² = y and the line y = x + 2.

Differentiate the following functions with respect to x:
$\tan^{-1}\Big(\frac{\sqrt{\text{x}}+\sqrt{\text{a}}}{1-\sqrt{\text{xa}}}\Big)$

Differentiate the following functions with respect to x:
$\frac{\sqrt{\text{x}^2+1}+\sqrt{\text{x}^2-1}}{\sqrt{\text{x}^2+1}-\sqrt{\text{x}^2-1}}$

Find the foot of perpendicular from the point (2, 3, 4) to the line $\frac{4-\text{x}}{2}=\frac{\text{y}}{6}=\frac{1-\text{z}}{3}.$ Also, find the perpendicular distance from the given point to the line.

In a hospital, there are 20 kidney dialysis machines and that the chance of any one of them to be out of service during a day is 0.02. Determine the probability that exactly 3 machines will be out of service on the same day.