Question

A six-sided number cube labeled 1 through 6 is rolled 200 times. An odd number is rolled 150 times. Compare the experimental probability of rolling an odd number with the theoretical probability of rolling an odd number and select one of the statements below that best describes the situation.

Answer 1

The theorectical probability is obtained using binomial distribution

Probabilty of getting an odd number is = n (O)/ n(T)

number of odd = {1,3,5} = 3

sample space ={ 1,2,3,4,5,6} = 6

Pr (O) = 3/6 = 1/2

If probability of success is (p) = 1/2

Probability of failure (q) = 1 - 1/2 = 1/2

For 200 trials , probability of getting odd 150 times is

`Pr^{}(xisODD)=^nC_{r\text{ }}* p^n* q^(n-r)`