Question

Zach scores a ringer 40, percent of the time that he throws a horseshoe. Let R be the number of throws it takes Zach to score his first ringer in a game. Assume the results of each throw are independent.
Find the probability that it takes Zach 555 or more throws to score his first ringer. P(R ≥ 5) = __________.

Answer 1

Answer:

0.1296

Step-by-step explanation:

The desired probability is calculated by using geometric probability distribution having the pdf of

P(X=r)=p*q^r-1 where x=1,2,3,....

The geometric distribution is used because experiment is repeated various number of times until the success is obtained.

Here p is the probability of success which is 0.4 in the given scenario as Zach scores a ringer 40% percent of time

We wish to calculate the probability that Zach throws 555 or more to achieve his first ringer that is

P(R≥5)=1-P(R<5)=1-P(R≤4)

P(R≤4)=P(R=1)+P(R=2)+P(R=3)+P(R=4)

P(R≤4)=0.4*0.6^0+0.4*0.6^1+0.4*0.6^2+0.4*0.6^3

P(R≤4)=0.4+0.4*0.6+0.4*0.36+0.4*0.216

P(R≤4)=0.8704

P(R≥5)=1-P(R≤4)=1-0.8704=0.1296.

So it is 12.96% chance that the Zach throws 555 or more to achieve his first ringer.

Answer 2

Answer:

.13

Step-by-step explanation: