This question is based on the geometric probability distribution.Therefore, it is 12.96% chances that the Zach throws 555 or more to achieve his first ringer.
Given:
Zach scores a ringer 40, percent of the time that he throws a horseshoe.
According to the question,
The probability is calculated by using geometric probability distribution having the pdf of
[tex]\bold{p \times q ^{x-1},\, x = 1,2,3,...}[/tex] where x = 1,2,3,....
This 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 situation as Zach scores a ringer 40% percent of time.
We would be 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.
Therefore, it is 12.96% chances that the Zach throws 555 or more to achieve his first ringer.
For more details, prefer this link:
https://brainly.com/question/10164132
