What is the likelihood of Courtney finishing at least three sudoku puzzles out of five?
To determine the likelihood of Courtney finishing at least three Sudoku puzzles out of five, we need to calculate the probability.
Step 1: Find the probability of successfully completing one Sudoku puzzle.
If Courtney has a success rate of completing a Sudoku puzzle, let's say 60%, the probability of success would be 0.6 or 60%.
Step 2: Determine the probability of successfully completing three, four, or five puzzles.
To find the probability of completing a specific number of puzzles, we can use the binomial probability formula. For each scenario (completing three, four, or five out of five puzzles), we will calculate the probability individually.
The binomial probability formula is:
P(X = k) = C(n, k) * p^k * (1-p)^(n-k)
Where:
P(X = k) is the probability of getting exactly k successes,
n is the number of trials,
k is the number of desired successes,
p is the probability of success in one trial, and
C(n, k) is the combination of n and k.
Step 3: Calculate the probability for each scenario.
To calculate the probability of completing three out of five puzzles, substitute the values into the formula as follows:
P(X = 3) = C(5, 3) * 0.6^3 * (1-0.6)^(5-3)
To calculate the probability of completing four out of five puzzles:
P(X = 4) = C(5, 4) * 0.6^4 * (1-0.6)^(5-4)
And for completing all five puzzles:
P(X = 5) = C(5, 5) * 0.6^5 * (1-0.6)^(5-5)
Step 4: Calculate the probability of finishing at least three puzzles.
To determine the likelihood of completing at least three puzzles, we need to consider all scenarios where Courtney completes three, four, or five puzzles. We can sum up the probabilities obtained in Step 3:
P(X >= 3) = P(X = 3) + P(X = 4) + P(X = 5)
By calculating this equation, we can find the likelihood of Courtney finishing at least three Sudoku puzzles out of five.