Based on past experiences, Miss Olenik knows that } of the mistakes on the essays she grades are grammar mistakes, } of the mistakes are spelling mistakes, and ½ of the mistakes are both grammar and spelling mistakes. If an essay is selected at random, what is the probability that the essay contains a grammar mistake or a spelling mistake?
To calculate the probability that the essay contains a grammar mistake or a spelling mistake, we can use the formula for the probability of the union of two events:
P(A or B) = P(A) + P(B) - P(A and B)
Where:
P(A) = probability of a grammar mistake = 3/4
P(B) = probability of a spelling mistake = 2/3
P(A and B) = probability of both grammar and spelling mistakes = 1/2
Plugging in the values:
P(grammar mistake or spelling mistake) = 3/4 + 2/3 - 1/2
P(grammar mistake or spelling mistake) = 9/12 + 8/12 - 6/12
P(grammar mistake or spelling mistake) = 11/12
Therefore, the probability that the essay contains a grammar mistake or a spelling mistake is 11/12.