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secondary 4 | A Maths
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Sonia
Sonia

secondary 4 chevron_right A Maths chevron_right Singapore

Hi!! Please help with this question:) Thanksss

Date Posted: 3 months ago
Views: 29
Eric Nicholas K
Eric Nicholas K
3 months ago
Hi Sonia!

For this question, you must consider the possible outcomes. Max has summed up all the answers accurately.

We assume that the three dice are fair (that is, nothing weird or unusual with the dice) and each die does not affect the other two dice.

There are a total of 6 x 6 x 6 = 216 possible outcomes of throws altogether. The possible outcomes are as follows.

First 1, second 1, third 1
First 1, second 1, third 2
First 1, second 1, third 3
First 1, second 1, third 4
First 1, second 1, third 5
First 1, second 1, third 6
First 1, second 2, third 1
First 1, second 2, third 2 and so on

...

First 6, second 6, third 5
First 6, second 6, third 6

Now, with this understanding, we proceed to answer the three parts.



(a) There is only one way in which the sum of the three numbers on the dice is 18.

"First 6, second 6, third 6"

This is one outcome out of 216 possible outcomes. Hence, the probability that the total sum is 18 is given by P (total sum is 18) = 1/216.



(b) There are six ways in which all three dice show the same number.

"First 1, second 1, third 1"
"First 2, second 2, third 2"
"First 3, second 3, third 3"
"First 4, second 4, third 4"
"First 5, second 5, third 5"
"First 6, second 6, third 6"

These account for six out of 216 possible outcomes. Hence, the probability that the three dice show the same number is given by P (all same number) = 6/216 which simplifies to 1/36.



(c) There are three ways in which the total sum is 17.

"First 5, second 6, third 6"
"First 6, second 5, third 6"
"First 6, second 6, third 5"

These account for three out of 216 possible outcomes. Hence, the probability that the three dice show the same number is given by P (total sum is 17) = 3/216 which simplifies to 1/72.



I hope the explanations are okay!

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Max
Max's answer
15 answers (A Helpful Person)
1st
I assume that each die is a fair six-sided one.

All the best!