Probabily of Dice

[KK]

Hello

This is regarding the simple probility question from startegy guide, where we are asked. What is the probability that sum of two dice will a 10 or lower.
In such cases. We normally find out all the pairs that add upto 10 or more. and divide it by 36

My question is will it be same scenario if the question is asking
- P of multiplication of pairs is 10
- P that the pairs multiplied are odd

Just thought about these variation. If anyone could throw some light.

Thanks in advance

[KK]

What i mean is that we consider duplicate pairs( 4,6), (6,4) is the case of sum. Will be do the same for the other two cases mentioned.

[esledge]

Yes, you have to consider duplicate pairs.

Think of it this way: Suppose the dice are different colors, 1 red and 1 blue. There are two distinct ways you can get a sum of 3: (1 on Red + 2 on Blue) and (2 on Red + 1 on Blue). Even if the dice both look the same, these two scenarios still exist.

The same approach would apply to the multiplication questions you suggested (good ones, by the way).

[KK]

Thanks Emily

Thats clear.

One last doubt on this
If given two Pairs
a=(1,2,3,4)
b = (4,5)

what is the probabilty that ab will be even.

Thanks...this will really clarify my doubts on this concept

[esledge]

In not entirely sure I understand your question, but I am taking it to mean that one value of a is selected from the set {1, 2, 3, 4} and one value of b is selected from the set {4, 5}. Then you multiply them together.

The long solution is to write out all possible a,b pairs and their products:
a*b = ab
1*4 = 4
1*5 = 5
2*4 = 8
2*5 = 10
3*4 = 12
3*5 = 15
4*4 = 16
4*5 = 20
Of the 8 products, 2 are odd, so the probability that ab is odd = 2/8 = 1/4.

The shorter way is to recognize there are 4 possible values for a, and 2 for b. That gives 4*2 = 8 outcomes. ab will only be odd when BOTH a and b are odd. There are 2 odds in the list for a, and 1 in the list for b. That gives 2*1 = 2 odd outcomes.