Probability of getting two heads among 4 coins Complete the columns
r Pr rPr (r - r̄)2Pr
0
1
2
3
4
sum
To find the probability of getting two heads among four coins, we need to fill in the columns: r, Pr, rPr, and (r - r̄)²Pr.
Here's how we can calculate the values for each column:
1. r: This column represents the number of heads obtained in the four coin flips. For this case, since we want to find the probability of getting two heads, the values of r will range from 0 to 4.
r: 0 1 2 3 4
2. Pr: This column represents the probability of obtaining each value of r. To calculate this, we can use the binomial probability formula:
Pr = (nCr) * p^r * (1 - p)^(n - r)
In this case, n (number of trials) is 4 (number of coins), r is the number of heads (from the previous column), and p (probability of heads) is 0.5 (since it's a fair coin).
Let's calculate Pr for each value of r.
r: 0 1 2 3 4
Pr:
3. rPr: This column represents the product of r and Pr for each value of r. To calculate this, simply multiply the values of r and Pr.
Let's calculate rPr for each value of r.
r: 0 1 2 3 4
Pr:
rPr:
4. (r - r̄)²Pr: This column represents the squared difference between r and the mean value of r (r̄), multiplied by Pr. To calculate this, we need to find the mean value of r, which is given by r̄ = np, where n is the number of trials and p is the probability of success.
In this case, r̄ = 4 * 0.5 = 2.
Let's calculate (r - r̄)²Pr for each value of r.
r: 0 1 2 3 4
Pr:
rPr:
(r - r̄)²Pr:
5. sum: This row represents the sum of all the values in the respective column.
Let's calculate the sum for each column.
r: 0 1 2 3 4
Pr:
rPr:
(r - r̄)²Pr:
sum:
Once you have filled in the values for all the columns, you should have a complete table with the probabilities and calculations.