Worksheet: Conditional Probability: Tree Diagrams

Q4:

The probability that it rains on a given day is 0.6. If it rains, the probability that a group of friends plays football is 0.2. If it does NOT rain, the probability that they play football rises to 0.8.

Q5:

A bag contains a total of nine marbles: three are blue and six are red. Michael randomly takes a marble from the bag, records its color, and puts it back in. He then repeats this process. He draws the following tree diagram.

Q7:

It is a little known fact that drugs have been used to enhance performance in sports since the original Olympic Games (776 to 393 BC). In fact, the origin of the word “doping” is thought to come from the Dutch word “doop,” which is a type of opium juice used by the ancient Greeks.

Currently, in all major sporting events, drug testing has become standard practice. However, it is known that not all those who test positive for drugs have actually taken drugs. This is called the “false positive effect.” Similarly, there is a “false negative effect,” where someone who tests negative for drugs has actually taken drugs.

In 2003, after anonymous testing of almost 1,500 players, the MLB (Major League Baseball) announced that approximately 6% of MLB players used performance-enhancing drugs. There was, however, a 5% chance that those who tested positive had not taken drugs and a 10% chance that those who had taken drugs tested negative.

Q10:

A bag contains a total of 12 marbles; 4 are green and the rest are yellow. Madison randomly takes a marble from the bag, records its color, and does not replace it. She then repeats this process a second time. She draws the following tree diagram.