SOLUTION: A box contains 5 tickets numbered 1 through 5. A ticket is selected at random and a die is rolled. a) List the elements of the sample space. b) What is the probability that the

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Question 1128279: A box contains 5 tickets numbered 1 through 5. A ticket is selected at random and a die is rolled.
a) List the elements of the sample space.
b) What is the probability that the sum of the numbers is even?
c) What is the probability that the number on the ticket is the same as the number on the die?
Answer by Quadratic1600(28) (Show Source):
You can put this solution on YOUR website!
Hi
This one is pretty tough!!!!
a) for the elements of the sample space surely they are 1 2 3 4 5 for the tickets and 1 2 3 4 5 6 for the dice
b) Ok for you to get an even number it is either even + even or odd + odd so
First part - Tickets
Chance of drawing even is 2/5
Chance of drawing odd is 3/5
Second part - dice
Chance of throwing even 3/6
Chance of throwing odd 3/6
So 2/5 x 3/6 and 3/5 x 3/6
2/5 x 3/6 = 1/5
3/5 x 3/6 = 3/10
1/5 + 3/10 = 1/2
So there is a 50% chance - However you could have just said if it isn't even then it is odd which would have been a lot more simple!!
c) Right ok for this one
You have a choice of 5 in the first part - 1 2 3 4 5
You have a choice of 6 in the second part - 1 2 3 4 5 6
If you pick 1 for example you have a 1/5 chance of selecting 1 the first time and a 1/6 chance in the second part so multiply 1/5 x 1/6 = 1/30
That is the probability for selecting two of the same.
Hope this has been of some help