Roll 2 dice and sum the spots. Then flip a coin that number of times. Find the exact probability of rolling a total of two if the experiment produced exactly as many heads as tails.
I recognize that it's a conditional probability but I don't know how to find the probability of getting exactly as many heads as tails.
Exactly!
In order to have an equal number of head & tails, E, you must have rolled an even sum: 2 4 6 8 10 or 12.
Here is an example. The probability of E and a sum of 4 is
.
So you must work out the following:
.
That is your denominator in the answer to this question which is:
.
Hello, fulltwist8!
This will take a while . . .
Roll two dice and sum the spots.
Then flip a coin that number of times.
Find the probability of rolling a total of 2
if there were exactly as many heads as tails.
We want:.
The numerator is: .
. .
. . With two tosses,
. . . . Hence: .
The denominator is: .
We must consider all twelve oucomes of the dice.
Hence: .
Therefore:.
I hope my arithmetic is correct . . . this time
Thanks for the heads-up, Plato!
.