# Thread: Need Urgent Help!! Probability Quesiton

1. ## Need Urgent Help!! Probability Quesiton

p=80% (chances of winning a game)
n=5 (number of games)
expected value of x=4

How do I find the variance and standard deviation of x?

And also, how do I find the probability that my opponent will win at least one game

Thanks!

2. ## Response

p=80% (chances of winning a game)
n=5 (number of games)
expected value of x=4

How do I find the variance and standard deviation of x?
well, variance is found by using V = n*p*(1-p)
V = 5*.80*.20 = 0.80

The standard deviation is found by taking the square root of the variance.
sigma = sqrt(V) = sqrt(0.80) = .8944

I'm gonna try to figure out the second part of the question now.

3. ## Response

p=80% (chances of winning a game)
n=5 (number of games)
expected value of x=4

How do I find the variance and standard deviation of x?

And also, how do I find the probability that my opponent will win at least one game

I think you would model your opponent winning at least one game as the probability of you winning at most 4 games:

P total = P(win 0) + P(win 1) + P(win 2) + P(win 3) + P(win4)

$
P(x\!=\!0) \;=\;{5\choose0}(0.8)^0(0.2)^5 \;=\;0.0003
$

$
P(x\!=\!1) \;=\;{5\choose1}(0.8)^1(0.2)^4 \;=\;0.0064
$

$
P(x\!=\!2) \;=\;{5\choose2}(0.8)^2(0.2)^3 \;=\;0.0512
$

$
P(x\!=\!3) \;=\;{5\choose3}(0.8)^3(0.2)^2 \;=\;0.2048
$

$
P(x\!=\!4) \;=\;{5\choose4}(0.8)^4(0.2)^1 \;=\;0.4096
$

Add all of these values to get: P total = 0.6723

4. Originally Posted by JohhnySD
solved! Thanks!
Do not delete questions that you think have been solved. Other members might want to look at the question. And it might not be as solved as you think ....

5. Originally Posted by ajj86
p=80% (chances of winning a game)
n=5 (number of games)
expected value of x=4

How do I find the variance and standard deviation of x?

well, variance is found by using V = n*p*(1-p)
V = 5*.80*.20 = 0.80

The standard deviation is found by taking the square root of the variance.
sigma = sqrt(V) = sqrt(0.80) = .8944

I'm gonna try to figure out the second part of the question now.
Please quote what you are responding to, so we do not have the present situation where we do not know what the original question was because the OP has deleted it.

Sorry I see that you have quoted it (if you use the quote button rather than the reply it will put the quoted text in a nice box).

Thanks

CB