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 0.0900
(round to four decimal places as needed.)

(b) the probability that nate gets a turkey is
(round to four decimal places as needed.)

Explanation:

Step1: Identify the probability of a single strike

The probability of getting a strike, \(p = 0.3\)

Step2: Use the multiplication rule for independent events

For independent events \(A\) and \(B\), \(P(A\cap B)=P(A)\times P(B)\). For three - strike (turkey), let each strike be an independent event.
The probability of getting a turkey (three strikes in a row) is \(P = p\times p\times p\)
Substitute \(p = 0.3\) into the formula: \(P=0.3\times0.3\times0.3\)

$$P = 0.3^{3}=0.0270$$

Answer:

\(0.0270\)