Question

statistics: if two dice are rolled, what is the probability of getting a sum of 5 if it is known that the sum is less than 10?

Answer 1

How many ways are there to get a sum that is less than 10 when you roll a pair of dice?

Answer 2

@Directrix is it 30?

Answer 3

How many ways are there to get a sum that is less than 10 when you roll a pair of dice?
>>is it 30? 30 is correct
The ways to get a sum less than 10 are marked in blue.
But, 30 is NOT the answer to the question.

Answer 4

if it is known that the sum is less than 10

Answer 5

There are 30 ways to get a sum less than 10

Of those 30 ways, how many of them have a sum of 5?

After that, we will be ready to find the probability.

Answer 6

@realsiege

Answer 7

The ways to get a sum of 5 are marked in black. How many sums of 5 are marked in black?

Answer 8

if two dice are rolled, what is the probability of getting a sum of 5 if it is known that the sum is less than 10?

It is known that the sum is less than 10. There are 30 ways to get a sum less than 10.

Assuming we counted correctly, the denominator of the probability fraction will be 30.

Of those 30 ways, we are interested in those that yield a sum of 5.

Answer 9

There are 4 throws that give a sum of 5.

P(getting a sum of 5 if it is known that the sum is less than 10) = 4/30 which is 2/15.

@realsiege Do you agree?

Answer 10

@Directrix sorry i just read this now

Answer 11

can i ask you another question? is this related to the formula p(a and b) = p(a) * p(b)? because i don't know how to use it.

Answer 12

The notifications are slow to show up on the screen. No worries.
Please check to see if you agree that there are 4 ways to get a sum of 5.

Answer 13

This is conditional probability but we did not use that formula to get the answer.

We counted the ways to get less than 10 and selected the number of ways to get a sum of 5.

Answer 14

>>is this related to the formula p(a and b) = p(a) * p(b)?

NOT the condiional probability formula ^^^

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This formula: p(a and b) = p(a) * p(b) was not used here.

It applies to a different sort of probability problem to the best of my knowledge.

Answer 15

oh alright,

so is there any way to count it faster or do i have to draw charts for this type of question?