Question

I ett laboratorium vet man av erfarenhet att ett experiment lyckas i 8 falla av 10, och att experiment lyckas oberoende av varandra.

a) Under en vecka genomfördes 25 experiment. Vad är sannolikheten att högst 2 experiment misslyckades?

b) Under ett år genomfördes 1100 experiment. Uppskatta sannolikheten att 900 eller fler experiment lyckades

Answer 1

We have

Probability of success = 8/10 = 0.80

a)

Here, we use Binomial distribution as :

n = Number of trials

p = probability of success

x = Number of sucess

In our case, X is number of times an experiment failed

So,

n = 25

p = probability of failure = 1 - probability of success = 1 - 0.80 = 0.20

Required probability = P(X 2) = P(X=0) + P(X=1) + P(X=2)

Note :

n! = n*(n-1)*(n-2)*.......................*1

0! = 1

So, solving above we get :

Similarly,

So,

Probability that at most 2 experiments failed = 0.0038 + 0.0236 + 0.0708 = 0.0982

b)

Here, since the sample size is large , we can use Binomial approximation to normal distribution

Number of successes will follow Normal distribution with parameters as :

Required probability = Probability that 900 or more experiments were successful = P(X>900)

We use Excel function "NORMSDIST()" as :

Hence,

Probability that 900 or more experiments were successful = P(X>900) = 0.066