Question

Suppose you roll two number cubes and pick a letter of the alphabet at random. Find the probability you roll 2 even numbers and pick one of the vowels a, e, i, o, or u.

Answer 1

Answer:

5 / 104

Step-by-step explanation:

Let A be the event that an even number is rolled on the first die (i.e. number cube).

Let B be the event that an even number is rolled on the second die.

Let C be the event that a vowel is selected.

Then:

P(A) = (# even numbers on die) / (# numbers on die) = 3/6 = 1/2

P(B) = 1/2  similarly

P(C) = (# vowels ) / (# letters ) = 5/26

These events are independent since the actions are carried out independently.

So...

P( roll 2 even numbers and pick a vowel )

= P( A and B and C )

= P(A) × P(B) × P(C)         [ this is the step that is using independence ]

= 1/2 × 1/2 × 5/26

= 5 / 104