# Thread: probability qn(not too hard!!)

1. ## probability qn(not too hard!!)

A secretary receives application forms for a current vacancy and has to check them for completeness before further processing is carried out on them. About one in every 20 is incomplete.
i) What is the probability that at least one incomplete form will occur in two successive forms that the secretary checks?
ii) In a batch of 100, what is the probability that at least one incomplete form will occur?
iii) How many form checks would result in a 10% chance of coming across an incomplete form?

2. Originally Posted by matty888
A secretary receives application forms for a current vacancy and has to check them for completeness before further processing is carried out on them. About one in every 20 is incomplete.
i) What is the probability that at least one incomplete form will occur in two successive forms that the secretary checks?
ii) In a batch of 100, what is the probability that at least one incomplete form will occur?
iii) How many form checks would result in a 10% chance of coming across an incomplete form?
i) $\left( \frac{1}{20} \right) \left( \frac{1}{20} \right) + \left( \frac{1}{20} \right) \left( \frac{19}{20} \right) + \left( \frac{19}{20} \right) \left( \frac{1}{20} \right)$

ii) 1 - Pr(none) $= 1 - \left( \frac{1}{20} \right)^{100}$.

iii) Let x be the random variable number of incomplete forms.

X ~ Binomial( p = 1/20, n = n).

You require Pr(X > 0) > 0.1 => 1 - Pr(X = 0) > 0.1 => Pr(X = 0) > 0.9.

So solve $\, \left( \frac{19}{20} \right)^n > 0.9 \,$ for the smallest integer value of n. I get n = 3.