Question

suppose that nate gets a strike when bowling (knocks all ten pins down on the first attempt) 30% of the time.
(a) what is the probability that nate gets two strikes in a row, assuming that attempts are independent?
(b) what is the probability that nate gets a turkey (three strikes in a row)?
(c) when events are independent, their complements are independent as well. use this result to determine the probability that nate gets a turkey, but fails to get a clover (four strikes in a row).

(a) the probability that nate gets two strikes in a row is
(round to four decimal places as needed.)

Explanation:

Step1: Identify the probability of a single strike

The probability of Nate getting a strike in one attempt is \(p = 0.3\).

Step2: Use the multiplication rule for independent events

For two independent events \(A\) and \(B\) (where \(A\) is the first - strike and \(B\) is the second - strike), the probability of \(A\) and \(B\) occurring is \(P(A\cap B)=P(A)\times P(B)\).
Since \(P(A) = P(B)=0.3\), the probability of two strikes in a row is \(P = 0.3\times0.3\).

Answer:

\(0.0900\)