IB AA HL May 2026 P1 TZA Q7

Reyn is investigating the fertility of a group of adult female foxes.

He has developed a clinical test that aims to identify whether or not a given fox is pregnant, and he wants to evaluate the reliability of this test.

Reyn knows that

• \(40\%\) of the foxes in the group are pregnant
• if a fox is pregnant, the probability that it will test positive is \(90\%\)
• if a fox is not pregnant, the probability it will test positive is \(20\%\).

1. Find the probability that a randomly selected fox from the group will test positive.[3]
2. Find the probability that a randomly selected fox from the group is pregnant, given that it tested positive.[3]