Suppose George wins 38​% of all thumb wars. ​(a) What is the proba

pro4ph5e4q2 2021-11-24 Answered
Suppose George wins 38​% of all thumb wars.
​(a) What is the probability that George wins two thumb wars in a​ row?
​(b) What is the probability that George wins four thumb wars in a​ row?
​(c) When events are​ independent, their complements are independent as well. Use this result to determine the probability that George wins four thumb wars in a​ row, but does not win five in a row.

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Expert Answer

Melinda Olson
Answered 2021-11-25 Author has 8941 answers
Probability(win game) \(\displaystyle={p}{\left({W}\right)}={0.34}\)
let \(\displaystyle{W}={w}\in,{L}={l}{o}{s}{e}\)
a) \(\displaystyle{p}{\left(\text{winning 2 wars simultaneously}\right)}={0.34}\cdot{0.34}={0.1156}\)
b) \(\displaystyle{p}{\left(\text{winning 4 games simultaneously}\right)}={0.34}\times{0.34}\times{0.34}\times{0.34}={0.34}^{{{4}}}={0.01336}\)
c)events are​ independent, their complements are independent as well.
A W has 0.34 probability. A L has 0.66 probability
So \(\displaystyle{p}{\left(\text{winning 4 in a row and failure in the 5th}\right)}={0.34}^{{{4}}}\times{0.66}={0.00882}\)
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