Draw A 6x6 Table First!

Probability Level 1

If I toss a fair 6-sided dice twice, which of the following is most likely to occur?

(A) : The sum of the numbers is 9.
(B) : The absolute difference between the numbers is 4.
(C) : The product of the numbers is 12.
(D) : The ratio between the larger number and the smaller number is 3.
(E) : All of the 4 above events are equally likely to occur

(A) (B) (C) (D) (E)

1 solution

Zee Ell
Aug 20, 2016

Relevant wiki: Probability - By Outcomes

The number and list of favourable outcomes:

"They are all equal" : 6 , { (1,1), (2, 2), (3, 3), (4, 4), (5, 5), (6, 6) }
"The ratio between the larger number and the smaller number is 3" : 4,

{ (1, 3), (3, 1), (2, 6), (6, 2) }
"The absolute difference between the numbers is 4": 4,

{ (1, 5), (5, 1), (2, 6), (6, 2) }
"The sum of the numbers is 9": 4,

{ (4, 5), (5, 4), (3, 6), (6, 3) }
"The product of the numbers is 12 ": 4,

{ (3, 4), (4, 3), (2, 6), (6, 2) }

We have the following probabilities:

4 favourable outcomes:

$p = \frac {4}{6^2} = \frac {4}{36} = \frac {1}{9}$

6 favourable outcomes:

$p = \frac {6}{6^2} = \frac {6}{36} = \frac {1}{6}$

Therefore, the event which occurs most frequently amongst the listed options is:

$\boxed { \text {They are all equal } }$

I believe "They are all equal" was referring to the probabilities of the previously listed items are the same, which you did show to be true.

Seth Christman - 4 years, 9 months ago

Draw A 6x6 Table First!

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