Question

I didn't understand that after (0.91)n _2/3 .....how to solve using calculator to get 5 and why 5 is the answer? why

Answer 1

Given p = 0.09 (success) 

q = 0.91 (failure) 

We have to find number of trials ‘n.’ 

According to the problem, 

P(X ≥ 1 ) > 1/3 

(We must have atleast one success) 

1 – P(X < 1) > 1/3 

1 – P(X = 0) > 1/3 

(or) P(X = 0) < 2/3 

Using p.m.f, we have, 

ⁿC₀(0.09) ⁰ (0.91) ⁿ < 2/3

(0.91)ⁿ < 2/3

we can use log tables to calculate (or) by trial method try for n = 1, 2,…… using calculator. 

We observe that (0.91)⁵ < 2/3 but (0.91)⁴ = 0.6857 > 2/3. Thus we need a minimum of 5 trials or more.