Answer:
a) 11/100
b) 60 times
Step-by-step explanation:
a)
We want to find the probability that a 3 will be rolled.
Probability = # of favorable outcomes / total # of outcomes.
Here the number of favorable outcomes will be the number of times a 3 was rolled and the total number of outcomes will simply be the # of times that the dice was rolled which can be calculated by finding the sum of the frequencies of each number.
So # of favorable outcomes = 11 ( as the dice was rolled on a 3 11 times.)
And the total number of outcomes would be 100 ( the sum of the frequencies , 12 + 35 + 11 + 23 + 7 + 12 = 100 )
So the probability of rolling a 3 would be 11/100
b)
For this part we want to find the expected times that a 6 would be rolled if we rolled the die 500 more times.
To calculate this we simply find the probability of rolling a 6 and then multiply that by 500.
So again probability = # of favorable outcomes / total # of outcomes.
Here # of favorable outcomes is frequency of rolling a 6 which would be 12 and the total number of outcomes is 100 as we found out during the last part.
So the probability of rolling a 6 is 12/100 or 3/25
We then multiply this by 500 to find the expected number of times a 6 would be rolled if the dice was rolled 500 more times
So our answer = 3/25 × 500 = 60 times
