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You roll two regular six-sided dice. Which event is more likely: A. You roll seven (i.e., the dice add up to seven). B. You roll doubles (i.e., both dice show the same number). Show or explain your thinking.

Answer :

Given:

A regular six-sided dice.

The probability of each number = 1/6

You roll two regular six-sided dice.

If we calculate the probability of the dice add up to seven

The seven will come for the following events

1 + 6

2 + 5

3 + 4

4 + 3

5 + 2

6 + 1

So, the total probability =

[tex]7\cdot(\frac{1}{6})^2=\frac{7}{36}[/tex]

Now, calculate the probability when both dice show the same number

So, the events will be:

1 + 1

2 + 2

3 + 3

4 + 4

5 + 5

6 + 6

So, the total probability =

[tex]6\cdot(\frac{1}{6})^2=\frac{6}{36}[/tex]

By comparing the results:

[tex]\frac{7}{36}>\frac{6}{36}[/tex]

So, the answer will be the event that is more like is:

A. You roll seven

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