If this die is rolled once, what is the probability that the outcome will be a 2 or a 4?

Question

A die is loaded so that it is equally likely to roll a 1 or a 2. Rolling a 3 or a 4 is also equally likely, and each of these is twice as likely as rolling a 1. Finally, rolling a 5 or a 6 is equally likely and each of these is 3 times as likely as rolling a 3.

a. 1/6
b. 1/4
c. 5/12
d. 7/18
e. none of the others

Answer 1

Think of the die as containing one 1, one 2, two 3s, two 4s, six 5s, and six 6s.

This way, the probability of rolling a 3 is 2/18 = 1/9 and the probability of rolling a 5 is 6/18 = 1/3, which is three times as likely as 1/9.

Now, since there is only one 2 present on the die, the chance of rolling a two is 1/18. Since there are two 4s on the die, the chance of rolling a 4 is 2/18. Add these two probabilities together to get:
1/18 + 2/18 = 3/18 = 1/6

The answer is (a) 1/6

Good luck, I hope this helps!

Answer 2

if your qn is whats the prob of rolling a 2 or 4 , it'd be 2/6

because 1/6 + 1/6 = 2/6 = 1/3

prob of rolling 1 or 2 is 2/18

prob of rolling 3 o 4 is 4/18

prob of rolling 5 or 6 is 12/18

hope i;m right .


2/18 + 4/18 = 6/18 = 1/3

option e

Answer 3

Ok, first of all:

let the probability of rolling either 1/2 = x

therefore,
the probability of rolling either 3/4 is 2x
the probability of rolling either 5/6 is 3*2x = 6x

NOTE: the probability of rolling either 1 or 2 is x. But the question only wants the probability of rolling a 2, so its x/2.

likewise, the question only wants the probability of rolling a 4, so its 2x/2 = x.

now, the probability of rolling a 2 = (x/2)/(9x) => 1/18.
the probability of rolling a 4 = (x)/(9x) = 1/9.

Adding these two probabilities up gives you the probability of getting either a 2 or a 4.

so P(2 or 4) = (1/18) + (1/9)
P(2 or 4) = 3/18 => 1/6

so your answer is a.

Answer 4

Well, first, I have a headache from thinking this early in the morning. I came up with "e" 3/18. From the way I figure it, there is one chance each for 1 or 2 to come up. Three or four are twice as likely so there are four chances for them. Five and six are three times as likely so there are 12 chances for them. That totals 18 chances. Of that number 2 would likely roll once, number four would like roll twice equalling three out of 18 or 3/18.