what is the probability of throwing 7 three times in a row, and throwing three 2's and throwing 3, then 4, then 5  on a pair of dice?  this involves throwing a pair of dice and has to do with...

what is the probability of throwing 7 three times in a row, and throwing three 2's and throwing 3, then 4, then 5  on a pair of dice?  

this involves throwing a pair of dice and has to do with basic law of probability

Expert Answers
embizze eNotes educator| Certified Educator

To find the probability of all of the throws happening you multiply the probabilities of each throw.

(1) The probability of throwing three 7's in a row:

The probability of throwing a 7 is 1/6: the possible throws are (1,6),(2,5),(3
,4),(4,3),(5,2),(6,1). Note that (1,6) and (6,1) are different; think of throwing two different colored dies -- a erd 1 and blue 6 is different from a red 6 and blue 1.

The sample space has 36 possibilities. So the probability of a seven is 6/36=1/6.

The probability of throwing 3 7's in a row is `1/6*1/6*1/6=(1/6)^3=1/216`

(2) The probability of throwing three 2's in a row:

The probability of throwing a 2 is 1/36 -- there is only 1 way to roll a 2; both dice must show a 1.

The probability of throwing 3 2's in a row is `1/36*1/36*1/36=(1/36)^3=1/46656`

(3) Throwing a 3: `2/36=1/18` (2 ways to roll a 3 out of a sample space of 36)

(4) Throwing a 4: `3/36=1/12`

(5) Throwing a 5: `4/36=1/9`

The probability of throwing 3 2's, a 3, a 4, then a 5 is :

`1/46656*1/18*1/12*1/9 =1/90699264`

The probability of throwing three 7's and then the other throws is:

`1/216*1/90699264~~5.10x10^(-11)`