We need to find the probability of atleast one failure in 5 trails
Probability of success = 30% = 3/10
The opposite meaning of atleast one failure is all success (no failures)
Probability of (atleast one failure ) = 1- Probability ( success)
First we find probability of success
Formula for binomial distribution
[tex] nCr(p)^r (q)^{n-r} [/tex]
All success so n=5, r=5, p= 3/10, q= 1-p = 7/10
Probability (success) = [tex] 5C5 ( \frac{3}{10})^{5}( \frac{7}{10})^{5-5} [/tex]
= [tex] (\frac{3}{10}) ^ 5 [/tex]
Probability (atleat one failure) = 1 - [tex] (\frac{3}{10}) ^ 5 [/tex]
= 0.92224
= 92.2%
