JNU Doubt

[AS]

Consider a gambling game where you have to throw two dice simultaneously.you would gain Rs.2 for any even number that shows up and loose Re 1 for any odd number that shows up.what is expected gain or loss.

[Anjali]

AS , if here even and odd refers to the sum of the two nos on the dice , then the ans would be
18/36 * 2 - 18/36 * 1= 1/2
[ 18 pairs have sum as even and 18 have sum as odd , total no of pairs are 36 ]

[AS]

but sum of two nos hasnt mentioned in question....

[Homer Simpson]

I am getting 1 as answer.

According to the question, if i get say (1,2) - then shouldnt i receive payoff of 1 with probability 1/36? and for (3,3), wouldnt i get -2 payoff? They havent mentioned anything on sums per say.

[Granpa Simpson]

Is the answer 50paise..???

[Anjali]

Tsuki generally in such questions sum is asked. Still , Iam not sure .
And please have a look at jnu 2010 doubts posted by jack
@subhayu Iam getting Rs 1/2 = 50 paise !

[Granpa Simpson]

I am getting 50p too..!!!!

[AS]

if you assume sum of two no then ans should be 1/2. i think tsuki approach is right...

[Anakin Skywalker]

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[Anjali]

@Anirudh , I have got your two Even and two Odd cases , but not clear with one odd and one even . Please explain.
@Subhayu , I guess we are following the "sum" case , which maybe is not appropriate here.

[Anakin Skywalker]

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[Anjali]

Great anirudh ! Got it !
Btw , your solution suggests that the outcome that is 36 is redundant here . Is that so ?

[Anjali]

Anirudh have a look at these two questions :

[The Villain]

We can also do the quest in this manner
Total cases=36

Even even=9 cases
odd odd= 9 cases
od-even = 18 cases
So x can takes values..
4(2+2)...even cases
-2(-1-1)...odd cases
1(2-1)...odd even cases
So mean is=4*9/36-2*9/36+1*18/36=1

[Dreyfus]

I think payoff with (even,even) should be 2 only bcoz it is given that whenever dice shows even no. payoff is 2 as it is paid only once!
Similarly for (odd,odd) it should be -1 only!
But for (odd,even) it should be 2-1=1
What do u think guys?

[Anjali]

I guess 2 should be added twice.

[Dreyfus]

May b I m over thinking!

[ViV]

A6 (c)
(2/6)*30+(2/6)*30=10+10=20

A7 (d)

[Anjali]

Viv how did you do 6th ?

[akanksha]

hi anjali...the 27th q will be solved by binomial..where n=30
and prob of success ie p= 2/6( prob of even no. greater than 2)  +2/6( prob of odd no. less than 4 )
thus p=4/6
in binomial
expected value=np
solving this well get expected no. of trials as 20..
for the 26th q...
observations that lie within the 1st quarile=25 per cent
observations that lie within the 3rd quartile=75 %
hence the ans is 50 % (75-25)