Define the folowing terms. (a) Experimental unit (b) Treatment (c) Response variable (d) Factor (e) Placebo ( Confounding (a) De
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Since the dice are fair and the rolling are independent, each single outcome has probability 1/15. Every time we choose
We have and
, because the dice are fair.
Now we use the assumption of independence to claim that
Now, we simply have to count in how many ways we can obtain every possible outcome for the sum. Consider the attached table: we can see that we can obtain:
- 2 in a unique way (1+1)
- 3 in two possible ways (1+2, 2+1)
- 4 in three possible ways
- 5 in three possible ways
- 6 in three possible ways
- 7 in two possible ways
- 8 in a unique way
This implies that the probabilities of the outcomes of are the number of possible ways divided by 15: we can obtain 2 and 8 with probability 1/15, 3 and 7 with probability 2/15, and 4, 5 and 6 with probabilities 3/15=1/5
All we want to do is get an equation with just x on one side and no x's on the other.
We can use inverse operations to accomplish this.
First, bring bx to the left side. Subtract the 3.
Factor ax+bx to x(a+b). (this is pretty much reversing the distributive property)
Divide by a+b and you are left with just x on the left side as 4/(a+b).
We can use inverse operations to accomplish this.
First, bring bx to the left side. Subtract the 3.
Factor ax+bx to x(a+b). (this is pretty much reversing the distributive property)
Divide by a+b and you are left with just x on the left side as 4/(a+b).