Question

Sam rolled a die 75 times. On 39 of those rolls, he had a 6. Which statement is TRUE when the probabilities are compared?

A) The theoretical probability is twice the experimental probability.


B) The experimental probability and the theoretical probability are equal.


C) The theoretical probability is greater than the experimental probability.


D) The experimental probability is greater than the theoretical probability.

Answer 1

D) The experimental probability is greater than the theoretical probability.

Explanation:

the theoretical probability says that each option (1, 2, 3, 4, 5, 6) will be rolled an even amount of times. to work this out, divide the total number of rolls (75) by the total amount of possibilities (6)

75 ÷ 6 = 12.5

so, theoretical probability says that each number should be rolled 12.5 times. The question says that 6 was rolled 39 times.

Theoretical P(6) =
`(12.5)/(75)`

Experimental P(6) =
`(39)/(75)`

the experimental probability is greater than the theoretical probability

∴ the answer is D

I hope this was helpful :-)

Answer 2

D)The experimental probability is greater than the theoretical probability

Explanation:

Given:

75 times a die is rolled out of 39 times it got 6

To Find :

Which statement is true?

Solution:

The theoretical probability is given by the ,

Pt=No.of favorable outcomes/Total outcomes

Here favorable is getting 6 on the die

so how many times we can get 6 =1 time

Total outcomes =6

Pt=1/6

Pt=0.1667

Now for

The experimental Probability ,

Pe=Number times that event occur /Total no of trails

Here 39 times we get 6 and total no trails are 75

Pe=39/75

Pe=0.52

Hence we can say that Pe>Pt.