Question

3 Tony performs an experiment with a standardsix-sided number cube and records his resultsin the table.Result123456Occurrence182115172019Which statement about the results of Tony'sexperiment is accurate?A Tony is one-half as likely to roll a 4 as he is toroll a 1 or a 5 combined.B Tony is 75% as likely to roll a 3 as he is to rolla 5.C Tony is 90% as likely to roll a 5 as he is to rolla 1.D Tony is equally likely to roll a 2 or a4 combined as he is to roll a l or a 6

Answer 1

B; Tony is 75% as likely to roll a 3 as he is to roll a 5

Here, we want to select the correct statement based on the data presented

The total number of times the die was rolled is the sum of the occurrences

We have this as;

18 + 21 + 15 + 17 +20+19 = 110

Now let us get the individual probabilities for each of the possible result

The probability of each is the number of times the particular number occurred, divided by the total occurrence

So we have;

`P(1)\text{ = }(18)/(110),\text{ P(2) = }(21)/(110),\text{ P(3) = }(15)/(110),P(4)\text{ = }(17)/(110),P(5)\text{ = }(20)/(110),P(6)\text{ = }(19)/(110)`

Let us now take a look at the options;

A) The probability of rolling a five or 1 combined is the sum of botha nd we have that as;

`P(1\text{ or 5) = }(18)/(110)+(20)/(110)\text{ = }(38)/(110)`

Now, one-half the probability of 4 is the probability of 4 multiplied by one-half

That would be;

`(1)/(2)*(17)/(110)\text{ = }(17)/(220)`

Since these two are not the same , we can conclude that this option cannot be correct

B) Now here, what we are trying to say is that the probability of rolling a 3 multiplied by 3/4 equals the probability of rolling a five

This is actually correct;

The number of occurrence of 3 is 15 and the number of occurrence of 5 is 20

15 is 75% of 20 and thus, this option is correct