Question

A box contains six red pills and three blue pills. Morpheus selects one pill at random and gives it to Neo. He then selects another pill at random and gives it to Trinity. Compute your answers as probabilities to 4 decimal places (where possible). What is the probability that Neo was given a red pill? ___________________ Neo was given a red pill. What is the probability that Trinity was given a blue pill? ___________ What is the probability that neither was given red pills? ___________________ What is the probability that both were given red pills? ___________________ What is the probability that Neo was given a blue pill and Trinity was given a red pill? ___________ What is the probability that Neo was given a red pill and Trinity was given a blue pill?

Answer 1

1. Probability that Neo was given a red pill: 6 out of 9 pills are red, so the probability is 0.6667.

2. Probability that Trinity was given a blue pill: After Neo takes one pill, there are 8 pills left, 3 of which are blue. So the probability is 0.375.

3. Probability that neither was given red pills: To calculate this, we multiply the probability of Neo getting a blue pill (0.3333) by the probability of Trinity getting a blue pill (0.375). The result is 0.1249.

4. Probability that both were given red pills: We multiply the probability of Neo getting a red pill (0.6667) by itself to get the probability of both getting red pills, which is 0.4444.

5. Probability that Neo was given a blue pill and Trinity was given a red pill: The probability of Neo getting a blue pill is 0.3333, and the probability of Trinity getting a red pill is 0.6667. Multiplying these probabilities gives us 0.2222.