Question

A slot machine pays-off 15% of the time.

a) What is the probability that a little old lady wins at least once if she plays 2 times?

b) What is the probability that she wins at least once if she plays 30 times

Answer 1

Answer)

As there are fixed number of trials and probability of each and every trial is same and independent of each other

Here we need to use the binomial formula

P(r) = ncr*(p^r)*(1-p)^n-r

Ncr = n!/(r!*(n-r)!)

N! = N*n-1*n-2*n-3*n-4*n-5........till 1

For example 5! = 5*4*3*2*1

Special case is 0! = 1

P = probability of single trial = 0.15 (15%)

N = number of trials = 2

R = desired success = at least once

A)

We know that sum of all the probabilities is = 1

P(at least 1) = 1 - P(0) = 1 - 2c0*(0.15^0)*(1-0.15)^2-0

= 0.2775

B)

N = 30

P(at least 1) = 1 - 30c0*(0.15^0)*(1-0.15)^30-0 = 0.992369240405210512171914800043411349087022244930267333984375