In a particular species of bird, there is a 40% chance that a newly hatched egg will live to the age at which is can itself reproduce. Of the entire species, only about 25% of birds end up reproducing. What is the conditional probability that a bird reproduces, given that it lives to be old enough to do so?

ESP Experiment. A person has agreed to participate in an extrasensory perception (ESP) experiment. He is asked to randomly pick two numbers between 1 and 6. The second number must be different from the first. Let H= event the first number picked is a 3, and K= event the second number picked exceeds 4. Determine a. P(H). b. P(K| H). c. P(H&K). Find the probability that both numbers picked are d. less than 3. e. greater than 3.

7 Double checking A patient comes to a hospital with symptoms that, in 1% of all cases, indicate a certain rare disease. The test for this rare disease never gives false negatives; if the disease is present, the test result is always positive. However, it gives false positives with a 3% probability even when the disease is not present. Given that the test is positive, find the probability that the patient has the disease. The test comes back positive, so the doctor runs the test again with a different sample. You may assume that false positives occur independently in different samples. Given that the second test also comes back positive, find the probability that the patient has the disease.

Let A and B be two events such that the probability of B is 0.5 and the probability of both is 0.2. Find the probability of A given that B occurs.