# Lesson Worksheet: Conditional Probability: Tree Diagrams Mathematics

In this worksheet, we will practice using tree diagrams to calculate conditional probabilities.

Q1:

A bag contains 3 blue balls and 7 red balls. David selects 2 balls without replacement and draws the following tree diagram. Given that the first ball is red, find the value of that represents the probability that the second ball selected is red.

• A
• B
• C
• D
• E

Q2:

Jacob flips a coin and then rolls a six-sided die. He draws a tree diagram to represent this. Find the probability that the die showed a number less than 3 given that the coin showed tails.

• A
• B
• C
• D
• E

Q3:

A bag contains 22 red balls and 15 black balls. Two balls are drawn at random. Find the probability that the second ball is black given that the first ball is red. Give your answer to three decimal places.

Q4:

A company manufactures a product in two different plants, and . The company supplies three customers, , , and equally, each with 80 units a month. produces 10 units of this product per month and the company distributes this amount among the three customers , , and in percentages of , , and respectively. If you select a unit at random from a outlet, find the probability that it is produced by .

Q5:

A bag contains 3 pink marbles, 4 orange marbles, and 5 yellow marbles. Two marbles are selected without replacement. Using a tree diagram, find the probability that the second marble is yellow given that the first marble is not yellow.

• A
• B
• C
• D
• E

Q6:

The tree diagram below shows the likelihood that it rains or does not rain and whether students walk or do not walk to school. Find the probability that a student walks to school.

• A
• B
• C
• D
• E

Find the probability that it rains, given that a student walks to school.

• A
• B
• C
• D
• E

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.

Drug testing has become standard practice. In 2003, after anonymous testing of almost 1,500 players, the Major League Baseball (MLB) announced that approximately ‎ of MLB players used performance-enhancing drugs. They got this result taking into account that there was a ‎ chance that those who had not taken drugs tested positive (false-positive effect) and a ‎ chance that those who had taken drugs tested negative (false-negative effect).

Find the probability that an MLB player chosen at random had not taken drugs and tested positive. Round your answer to three decimal places if necessary.

Find the probability that an MLB player chosen at random had taken drugs and tested positive. Round your answer to three decimal places if necessary.

Find the probability that an MLB player chosen at random had positive test results. Round your answer to three decimal places if necessary.

Q8:

Jennifer travels to school by car or on foot.

The probability that she travels by car is 0.4 and the probability that she walks is 0.6.

If she travels by car, the probability that she is late is 0.2; if she travels on foot, the probability that she is late is 0.3. Using a tree diagram, calculate the probability that she is late given that she traveled by car.

Q9:

There are an unknown number of balls in the bag. There are 3 white balls and some black balls. Two balls are selected without replacement. If the probability of selecting a black ball, given that the first ball is white, is , how many black balls are there in the bag?

Q10:

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.

Work out the probability that it rains on a given day and the friends play football.

Work out the probability that it does NOT rain on a given day and the friends play football.

What is the probability that the friends will play football on a given day?