Question 21668: Consider the experiment of rolling two fair dice.
a. What is the probability that you get either: "snake eyes" of "double boxcars"?
b. What is the probability that the total number of points shown on these two dice is a perfect square?
c. What is the probability that the total number of points shown on these two dice is a prime number?
Answer by venugopalramana(3286)   (Show Source):
You can put this solution on YOUR website! SEE BELOW
Consider the experiment of rolling two fair dice.
a. What is the probability that you get either: "snake eyes" of "double boxcars"?
I TRUST YOU MEAN GETTING A ONE ON EAH DICE OR GETTING A TWO ON EACH DICE..PLEASE CONFIRM THIS NOMENCLTURE.IN ANY CASE YOU CN USE THE METHOD GIVN BELOW TO SOLVE ANY PROBLEM
LET US FIRST FIND OTAL NUMBER OF POSSIBILITEIES..FOR EACH NUMBER LIKE SAY 1 (OR 2 OR 3....)APPEARING ON DICE NO.ONE,THERE ARE 6 POSSIBILITIES OF GETTING NUMBERS 1 TO 6 ON DICE NO.TWO...SO THERE ARE 6*6=36 TOTAL POSSIBLE OUT COMES IN A THROW OF 2 DICE.....N=36
SUCCESSFULL OUT COMES ARE ONLY 2 NAMELY 1 AND 1 APPEARING OR 2 ND 2 APPEARING SO
S=2
PROBABILIY OF SUCCESS =S/N=2/36=1/18
b. What is the probability that the total number of points shown on these two dice is a perfect square?..TOTAL NUMBER OF POINTS ON 2 DICE WILL VARY FROM MIMNIMUM OF 1+1=2 TO 6+6 =12...F THESE PERFECT SQUARES ARE 4 AND 9 ONLY..
NOW WE CAN GET 4 BY 1+3,OR 2+2 OR 3+1...IN 3 WAYS
AND WE CN GET 9 BY 3+6,4+5,5+4,6+3....IN 4 WAYS
SO TOTAL SUCCESSFULL WAYS =3+4=7
SO PROBABILIY OF GETTING PERFECT SQUARE =7/36
c. What is the probability that the total number of points shown on these two dice is a prime number?....AS BOVE PIME NUMBERS BETWEEN 2 AND 12 ARE 2,3,5,7,11
2 CAN BE GOT BY 1+1........IN 1 WAY
3 CAN BE GOT BY 1+2,2+1.......2 WAYS
5 CAN BE GOT BY 1+4,2+3,3+2,4+1....4 WAYS
7 CAN BE GOT IN 1+6,2+5,3+4,4+3,5+2,6+1......6 WAYS
11 CN BE GOT IN 5+6,6+5...2 WAYS
SO TOTAL SUCCESSFULL WYS ARE 1+2+4+6+2=15 WAYS
SO PROBABILITY =15/36=5/12
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