Answer:
[tex](0.65)^5(0.35)[/tex] is the probability she first wins of the sixth ticket.
Step-by-step explanation:
We are given the following information:
We treat winning lottery as a success.
P(Success) = P(Winning) = 35% = 0.35
Thus, we can write
P(Failure) = P(Loosing the lottery) = 0.65
We have to find the probability she first wins of the sixth ticket.
That is we can write she want the success to occur at 6 position after 5 failures.
Let x be the random variable for the first win.
Then, X follows a geometric distribution and probability is given by:
[tex]P(X = k ) = (1-p)^kp[/tex]
where p is the probability of success and k is the failures that occur before the first success.
Thus, we can write
[tex]P(x =5) = (1-0.35)^5(0.35)\\P(x =5) = (0.65)^5(0.35) = 0.04[/tex]
Thus, 0.04 is the probability she first wins of the sixth ticket.
None of the given option gives the right probability.
