Question

Fair Dice

We roll a fair dice 10 times and register how many times we obtained 5.

(a) Find the probability to obtain 5 seven times.

(b) Estimate the number of fives that will come out with the probability 0.35.

(c) What is the probability of geting 30 fives when rolling a fair dice 45 times?

(d) How many fives will come out with a probability of 0.25, when rollong a fair dice 45 times?

Answer 1

When we roll a fair dice the probability of getting a five in one roll is

p = P(5) = 1/6

(a)

Let X is a random variable shows the number of fives in 10 rolls. Here X has binomial ditribution with parameters n=10 and p=1/6.

So the probability to obtain 5 seven times is

So the required probability is 0.0002.

(b)

Here we need to find x such that

Following table shows the binomial distribution (rounded to 2 decimal):

X	P(X=x)
0	0.16
1	0.32
2	0.29
3	0.16
4	0.05
5	0.01
6	0
7	0
8	0
9	0
10	0

From above table, we know that for 10 rolls, we have not any number of fives which come with probability 0.35.

The nearest number of fives is 1.

(c)

The probability of geting 30 fives when rolling a fair dice 45 times is

(d)

Here we need to find x such that

Following table shows the binomial distribution (rounded to 2 decimal):

X	P(X=x)
0	0
1	0
2	0.01
3	0.03
4	0.07
5	0.11
6	0.14
7	0.16
8	0.15
9	0.12
10	0.09
11	0.06
12	0.03
13	0.02
14	0.01
15	0
16	0
17	0
18	0

From above table, we know that for 45 rolls, we have not any number of fives which come with probability 0.25.