Question

Calculate the probabilities using geometric distribution

Round to 3 decimal places.

a. The first success will occur on the 6th trial with p=0.41
P(6)=

b. The first success will occur on the 9th trial with p=0.2
P(9)=

c. The first success will occur on the 12th trial with p=0.09
P(12)=

Answer 1

If X denotes the number of trials to get first success, then X ~ Geometric(p)

The probability mass function of X is

$P(X = x) = p(1-p)^{x-1},x=0,1,2,3,....$

a) X ~ Geometric(p = 0.41)

The probability that the first success will occur on the 6th trial

$= P(X = 6) = 0.41(1-0.41)^{6-1} = 0.0293119$

b) X ~ Geometric(p = 0.2)

The probability that the first success will occur on the 9th trial

$= P(X = 9) = 0.2(1-0.2)^{9-1} = 0.0335544$

c)  X ~ Geometric(p = 0.09)

The probability that the first success will occur on the 12th trial

$= P(X = 12) = 0.09(1-0.09)^{12-1} = 0.0318932$