7 Consider a sixsided die that has been designed so that all

7. Consider a six-sided die that has been designed so that all even numbers are equally likely, all odd numbers are equally likely, but an even number is twice as likely as an odd number. What is the probability that this die lands 2?

Solution

Note that

P(even) + P(odd) = 1

As

P(even) = 2 P(odd)

Then

2P(odd) + P(odd) = 1

P(odd) = 1/3

Thus,

P(even) = 2/3.

Now, there are three evens, 2, 4, 6. Thus,

P(2|even) = 1/3.

Thus,

P(2) = P(even) P(2|even)

= (2/3)(1/3)

= 2/9 = 0.22222222222 [ANSWER]