MHB Macie's question at Yahoo Answers regarding binomial probability

AI Thread Summary
The discussion focuses on calculating the probability of rolling 10 or fewer sixes when a die is thrown 60 times using the binomial probability formula. The parameters include n=60 trials and p=1/6 for rolling a six. The total probability for getting between 0 to 10 sixes is calculated by summing the probabilities for each outcome from 0 to 10. The final computed probability is approximately 0.5834. This calculation can be efficiently performed using tools like Wolfram|Alpha.
MarkFL
Gold Member
MHB
Messages
13,284
Reaction score
12
Here is the question:

A die is thrown 60 times. What is the probability of 10 or fewer "sixes" ?

I have posted a link there to this topic so the OP can see my work.
 
Mathematics news on Phys.org
Hello Macie,

We want to use the binomial probability formula:

$$P(x)={n \choose x}p^x(1-p)^{n-x}$$

where:

$$0\le x\le10\in\mathbb{Z}$$

$$n=60$$ is the number of trials

$$p=\frac{1}{6}$$ is the probability of rolling a six in any trial.

We want to find the probability that we get zero 6's or 1 6 or 2 6's or...10 6's. So we want to sum up the probabilities for $x=0$ to $x=10$. With the aid of technology, we find:

$$P(X)=\sum_{x=0}^{10}\left({60 \choose x}\left(\frac{1}{6} \right)^x\left(\frac{5}{6} \right)^{60-x} \right)=\frac{9504082209854658458425546996295452117919921875}{16291225993563085829774250757924867955220283392}$$

$$P(X)\approx0.583386555045634235343489438735516181052152146974030836906911$$

I entered the command:

sum of nCr(60,k)(1/6)^k(5/6)^(60-k) for k=0 to 10

at Wolfram|Alpha: Computational Knowledge Engine
 
Seemingly by some mathematical coincidence, a hexagon of sides 2,2,7,7, 11, and 11 can be inscribed in a circle of radius 7. The other day I saw a math problem on line, which they said came from a Polish Olympiad, where you compute the length x of the 3rd side which is the same as the radius, so that the sides of length 2,x, and 11 are inscribed on the arc of a semi-circle. The law of cosines applied twice gives the answer for x of exactly 7, but the arithmetic is so complex that the...
Back
Top