SOLUTION: Consider the event of getting a head in 4tosses of a fair coin. Let X be the random variable representing the number of heads minus the number of tails. Create a Probability Distri

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Question 1205515: Consider the event of getting a head in 4tosses of a fair coin. Let X be the random variable representing the number of heads minus the number of tails. Create a Probability Distribution table for the random variable X.
Found 2 solutions by greenestamps, math_tutor2020:
Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


The statement of the problem is faulty.

The event of getting a head in 4 tosses of a fair coin is a single event. "A head" means there is one head, so there are 3 tails, and the number of heads minus the number of tails is 1-3 = -2.

So the very uninteresting probability distribution is

P(-2) = 1

Answer by math_tutor2020(3817) About Me  (Show Source):
You can put this solution on YOUR website!

The probability distribution is
# heads# tailsX = heads-tailsP(X)
4041/16
3124/16
2206/16
13-24/16
04-41/16


Below I'll explain how I got each P(X) probability value.

There are n = 4 tosses of the coin.
That gives 2^n = 2^4 = 16 different outcomes.

Of those outcomes, there's only one way to get all heads. Same goes for all tails. That explains the 1/16 probability values for the first and last rows.

If there are 3 heads, then there are 4 ways to have this situation. This is because there are 4 places to put the tail. Those 4 outcomes are:
  1. HHHT
  2. HHTH
  3. HTHH
  4. THHH
Due to symmetry, the same idea applies if there are 3 tails.
So that's how we get a probability of 4/16 for the 2nd row and 2nd to last row.

If there are 2 heads, then there are 4C2 = 6 ways to arrange them. The 4C2 refers to the nCr combination formula. Such values can be found in Pascal's Triangle. The 6 ways to have 2 heads and 2 tails are listed here
  1. HHTT
  2. HTTH
  3. HTHT
  4. TTHH
  5. THTH
  6. THHT
So that's how I'm getting 6/16 for the probability of 2 heads.

I have not reduced the fractions in the P(X) column because I wanted to keep the denominators the same. But if you wanted you could reduce the fractions.
4/16 = 1/4
6/16 = 3/8

Or you can convert all the fractions to decimal form.
1/16 = 0.0625
4/16 = 1/4 = 0.25
6/16 = 3/8 = 0.375
Each decimal value is exact.

Two things to notice:
  • Each P(X) value is between 0 and 1.
  • The P(X) values add to 1.