Question

Researchers often enter a lot of data into statistical software programs. The probability of making zero to two errors per 1,000 keystrokes is 0.58, and the probability of making three to five errors per 1,000 keystrokes is 0.27. Find the probabilities (per 1,000 keystrokes) associated with each of the following.

At Most 2 Errors

At least 3 Errors

At most 5 errors

More than 5 errors

Answer 1

X: Number of error made in 1,000 keystrokes

Probability of making zero to two errors per 1,000 keystrokes is 0.58

P(X=0 or X=1 or X=2 ) = P(X2) = 0.58

Probability of making three to five errors per 1,000 keystrokes is 0.27

P(X=3 or X=4 or X=5) = P(3X5) = 0.27

probability (per 1,000 keystrokes) of making at Most 2 Errors = P(X2) = 0.58

probability (per 1,000 keystrokes) of making at least 3 = P(X3) = 1- P(X2) = 1-0.58 = 0.42

probability (per 1,000 keystrokes) of making at most 5 = P(X5) = P(X2) + P(3X5) = 0.58 + 0.27 = 0.85

probability (per 1,000 keystrokes) of more than 5 = P(X>5) = 1-P(X5) = 1-0.85 = 0.15