Suppose you roll a six-sided die two times hoping to get two numbers whose sum is even. What is the sample space? How many favorable outcomes are there?

Question

anonymous · Answer

9/36

anonymous · Answer

S = 36

anonymous · Answer

sample space has 36 elements !!!

11 12  13  14  15  16
21 ---------------
31 ----------------
41 ----------------
51 ----------------
61 ----------------

make it yourself and then see how many of them fulfil your condition and then get your answer

anonymous · Answer

sample space is 36
favorable outcomes are 12/36 = 1/3

anonymous · Answer

favourable outcomes are 18 !!!

anonymous · Answer

well it depends on whether you allow for repetition or not

anonymous · Answer

27/36

anonymous · Answer

@kanwar

27  favourable outcomes ????? pls count again

anonymous · Answer

it says nothing about repeating

all it says is sum has to be even

anonymous · Answer

favorable out comes are 1-1
 1-3
 1-5
 2-2
 2-4
 2-6
 3-3
 3-5
 4-4
 4-6
 5-5
 6-6

anonymous · Answer

11 13 15 22 24 26 31 33 35 42 44 46 51 53 55 62 64 and 66  i.e 18 fAVOURABLE OUTCOMES

anonymous · Answer

@dhatraditya

u missed some !!!

anonymous · Answer

Yes, harkirat is correct, you have to count the inverse occurences (ie 1-3 and 3-1) since they are separate events.

anonymous · Answer

right, harkirat is right, but I didn't consider the repetitious ones.
I am assuming 1-3 is the same as 3-1

anonymous · Answer

do a sample space diagram.

                      numbers on 1st dice.
                     1           2             3             4             5            6
________________________________________________________________
n              1|  1+1=2   2+1=3    4             5             6            7
u         2     |
m   o    n   2|    3         4             5             6             7             8
b    n    d    |
e              3|     4        5              6             7             8             9 
r           d    |
s           i   4|     5        6              7             8              9           10      
            c     |
            e   5|     6        7             8              9            10           11
                   |
                 6|     7        8            9              10           11           12

so we are adding the top number to the side number to get the entries in
the table.

Total amount of even numbers in the table is 18
total amount of entries is in the table is 36.
Probability of getting an even answer on summing the die totals =18/36 = 1/2

anonymous · Answer

if not, and you treat the two dice as distinct events, then yes, harkirat is right

anonymous · Answer

no no 13 is never same as 31, they r distinctly separate events

anonymous · Answer

Also it makes intuitive sense that half of the possible outcomes are even when both dice have equal numbers even and odd numbers on them.