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 0.0270
(round to four decimal places as needed)

(c) the probability that nate gets a turkey, but fails to get a clover is
(round to four decimal places as needed)

Explanation:

Step1: Determine the probability of a strike

Given that the probability of getting a strike \(P(S)=0.3\)

Step2: Calculate the probability of getting a turkey (three strikes) and not a clover (four strikes)

The probability of getting a turkey (three strikes) is \(P(\text{turkey})=(0.3)^3\). The probability of getting a clover (four strikes) is \(P(\text{clover})=(0.3)^4\).
We want \(P = P(\text{turkey})\times(1 - P(S))\) (because after three strikes, the fourth is not a strike).
Substitute \(P(S) = 0.3\) into the formula:

$$
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$$

Step3: Compute the final value

\(0.027\times0.7 = 0.0189\)

Answer:

\(0.0189\)