Statistics

Question

Roll two fair dice. Each die has six faces. a. Find the probability that either a three or four will be on first roll, followed by an even number. b. Find the probability that the sum of the two rolls is seven.

Answer 1

a. Find the probability that either a three or four will be on first roll, followed by an even number.

 

Since these are two independent events, we can multiply the independent probabilities to gain their combined probability of occurring.

P(3 or 4) * P(even number)

= 2/6 * 3/6

= 6/36

= 1/6

 

b. Find the probability that the sum of the two rolls is seven

 

Here we need to figure out all of the possibilities for sums of rolling two fair die. I cheated a bit and looked this up on this website here (http://gwydir.demon.co.uk/jo/probability/calcdice.htm), but you may need to be able to figure this out for yourself for a test, so make sure you understand it.

 

There's 36 possible combinations of rolls of two die and six of them are sevens.  So the odds are 6/36 = 1/6.