probability question, Find the probability that Anna will,

Question

1. Question:Anna predicts that she has an 80% chance of passing Science and a 90% chance of passing Geography.

Find the probability that Anna will,

a) pass both science and geography (is the answer 72%)

b) pass science but will fail geography ( 98%?)

c) fail both science and geography (2%?)

Answer 1

P(fail science) = 1 - P(pass science) = 0.2

P(fail geography) = 1 - P(pass geography) = 0.1

Assume taking tests are independent events

P(pass science and geography) = P(pass science)*P(pass geography) = 0.8 * 0.9 = 0.72

P(pass science and fail geography) = P(pass science(*P(fail geography) = 0.8 *0.1 = 0.08

P(fail science and geography) = P(fail science) * P(fail geography) = 0.2 * 0.1 = 0.02