You roll a pair of four-sided dice and record the sum. List all of the possible sums and determine the probability of rolling a sum of 7

You roll a pair of four-sided dice and record the sum. List all of the possible sums and determine the probability of rolling a sum of 7

393k points

You roll a pair of four-sided dice and record the sum. List all of the possible sums and determine the probability of rolling a sum of 7.

List all the possible sums.

What is the probability of rolling a sum of 7?

You roll
bhdrkn

403.4k points

You roll two die in this scenario, each with four sides. So the possible sums are given by,

• 1+1 = 2
• 1+2 = 3
• 2+1 = 3
• 2+2 = 4
• 2+3 = 5
• 3+2 = 5

etc..

So the possible sums are 2,3,4,5,6,7,8

The probability of rolling a 7 is found using,

$$P(E)=\frac{n(E)}{n(T)}$$

which is the number of ways of rolling a 7, divided by the total number of possible outcomes.

There are only two ways of rolling a 7:

• rolling a 3 and 4
• rolling a 4 and 3

And the number of possible outcomes is $4\times 4=16$ therefore the probability of rolling a 7 is,

$$P(7) = \frac{2}{16} = \frac{1}{8} = 0.125$$

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