Advertisement Remove all ads

# Solve the following problem : The probability that a bomb will hit the target is 0.8. Find the probability that, out of 5 bombs, exactly 2 will miss the target. - Mathematics and Statistics

Sum

Solve the following problem :

The probability that a bomb will hit the target is 0.8. Find the probability that, out of 5 bombs, exactly 2 will miss the target.

Advertisement Remove all ads

#### Solution

Let X denote the number of bombs hitting the target.
P(bomb hits the target) = p = 0.8
∴ q = 1 – p = 1 – 0.8 = 0.2
Given, n = 5
∴ X ~ B(5, 0.8)
The p.m.f. of X is given by
P(X = x) ""^5"C"_x (0.8)^x (0.2)^(5 - x), x = 0, 1,...,5
∴ P(exactly two will miss the target)
= P(exactly three will hit the target)
= P(X = 3)
= ""^5"C"_3 (0.8)^3 (0.2)^(2)

= (5!)/(3! xx 2!)(4/5)^3 (1/5)^2

= (5 xx 4 xx 3!)/(2 xx 1 xx 3!) xx (4^3/5^5)

= 10(4^3/5^5).

Is there an error in this question or solution?
Advertisement Remove all ads

#### APPEARS IN

Balbharati Mathematics and Statistics 2 (Commerce) 12th Standard HSC Maharashtra State Board
Chapter 8 Probability Distributions
Part II | Q 1.04 | Page 156
Advertisement Remove all ads

#### Video TutorialsVIEW ALL 

Advertisement Remove all ads
Share
Notifications

View all notifications

Forgot password?