Question

Jason rolled a six-sided fair die
30
times and recorded the number five
8
times. Based on this information, which statement is true?


If he rolls the die
30
more times, he will give the number five
8
more times.


The probability of rolling the number five is
4
15
.


If he rolls the die
30
more times, he is likely to roll the number five
5
more times


The probability of rolling the number
5
is
1
3
.

Answer 1

The third statement is true.

Reason: A fair six-sided die has probability 1/6 of rolling a 5. In 30 rolls the expected number of 5s is 30*(1/6) = 5, so in another 30 rolls you'd expect about 5 more fives (not guaranteed). The 8 observed in the first 30 is just sampling variation.