Answer:
Option A - 0.003
Step-by-step explanation:
Given: Probability of success = 63%= 0.63
Probability of failure = 1-0.63=0.37
To find: Probability that the first success occurs after the sixth trial
Formula for calculating geometric probabilities:
If P(X >n) or the probability that it takes more than a certain number of trials to achieve the first success.
[tex]P(X>n)=(1-p)^n[/tex]
where, X has a geometric distribution,p is the probability of success and (1-p) is the failure and possible values of X are 1, 2, 3, ....
Now, put values p=0.63, (1-p)= 0.37 , n=6 in the formula
[tex]P(X>n)=(1-p)^n[/tex]
[tex]P(X>6)=(0.37)^6[/tex]
[tex]P(X>6)=0.0025[/tex]
[tex]P(X>6)=0.003[/tex]
Therefore, Option A is correct
