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

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.

## Want to know more about Probability?

• Questions are typically answered in as fast as 30 minutes

### Solve your problem for the price of one coffee

• Math expert for every subject
• Pay only if we can solve it

Melinda Olson
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 $$\displaystyle{p}{\left(\text{winning 4 in a row and failure in the 5th}\right)}={0.34}^{{{4}}}\times{0.66}={0.00882}$$