Zoe has a chance of receiving an A grade in statistics, a chance of receiving an A grade in mathematics, and a chance of receiving A grades in both statistics and mathematics. Find the probability that she receives an A in statistics or mathematics (or both).

Question:

Zoe has a 67% chance of receiving an A grade in statistics, a 51% chance of receiving an A grade in mathematics, and a 41% chance of receiving A grades in both statistics and mathematics. Find the probability that she receives an A in statistics or mathematics (or both).

Answer:

The answer to the question is;

The probability that she receives an A in statistics or mathematics (or both) is 77%. which is a probability of 0.77.

Step-by-step explanation:

To solve the question we have

P (S) = Chance of having A grade in statistics = 67 %

P (A) = Chance of having A grade in mathematics = 51 %

P (S) ∩P (A) = Chance of having A grade in both mathematics and statistics

= 41 %

Therefore the chance of having an A grade in only statistics is given by

P (S) - P (S) ∩P (A) = 67 - 41 = 26 % similarly

The chance of having an A grade in only mathematics is given by

P (A) - P (S) ∩P (A) = 51 - 41 = 10 %

Therefore the chance of having an A grade in statistics or mathematics (or both) is given by

P (S) - P (S) ∩P (A) + P (A) - P (S) ∩P (A) + P (S) ∩P (A)

= 26 + 10 + 41 = 77%