p=80% (chance of winning a game)
n=5 (number of games)
What is the probability that you will win at least 4 games (find the probability that x is greater than or equal to 4).
Hello, JohhnySD!
This is a Binomial probability.
p = 80% (chance of winning a game)
n = 5 (number of games)
What is the probability that you will win at least 4 games?
"Win at least 4 games" means "Win 4 games or Win 5 games."
. . $\displaystyle P(x\!=\!4) \;=\;{5\choose4}(0.8)^4(0.2)^1 \;=\;0.4096$
. . $\displaystyle P(x\!=\!5) \;=\;{5\choose5}(0.8)^5(0.2)^0 \;=\;0.32768$
Therefore: .$\displaystyle P(x \geq 4) \;=\;0.4096 + 0.32768 \;=\;0.73728 \;\approx\;73.7$%