I need help with figuring out what method to use to figure out this problem..
Here is the problem.
A fair coin was flipped 10 times; compute the chance that the number of heads is less than 4.
Please help me solve this! Thank you.
You need the Binomial Probability formula . . . several times.
A fair coin was flipped 10 times.
Compute the chance that the number of heads is less than 4.
"Less than 4 heads" means: 3 heads or 2 heads or 1 head or no heads.
We must find these separate probabilities . . . and add them.
Is there a way of figuring this out without doing all of that computing?
Another question asked is A fair coin was flipped 100 times, compute the chance that the number of heads is less than 40. I can't imagine doing an equation for every single one through 40!
Such that can be programmed into a computer.
I presume there is a way to do it via normal distribution but I never learned probability.
My approah is to find,
(infamous Gamma function).
I know it looks ugly but programs can do this easily. Taking integral by Simpon's rule. Thus, all you need to do is tell your computer to find this integral.
Could i suggest to use Normal distribution method. Normal distribution can be used as an approximation to the binomial distribution (as suggested by soroban) when:
- Number of trail is large (greater than 30)
- probability of success at any trail is not too small or large (the closer to 0.5 the better)
Here you go:
First you will need to find the expected mean: number of trail x probability of success at any trail = 100 x 0.5 = 50
Next, find the standard deviation = squaroot 100 x 0.5 x 0.5 = 5
Then you can find the probability by; P(z < (39.5 - 50)/5) = P(z < -2.1) =0.0179 (find from Normal disribution tables)
approximation and the exact value. These are 0.0179, 0.0227 and 0.0176
Though if we apply a continuity correction to the integral above so we
integrate from -0.5 to 39.5 the integral changes from 0.0227 to 0.0178
which is indistinguishable from the normal approximation in this case.
I think the problem is that if you have the computational resources to
to the integral, you also have the resources to do the exact calculation.