Lesson: Conditional Probability: Tree Diagrams Mathematics

In this lesson, we will learn how to use tree diagrams to calculate conditional probabilities.

Lesson Plan

Lesson Explainer

Lesson Worksheet

Q1:

A bag contains 27 white balls and 6 black balls. If 2 balls are drawn consecutively without replacement, what is the probability that the second ball is black given that the first is black?

Q2:

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?

Q3:

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 6%β€Ž of MLB players used performance-enhancing drugs. They got this result taking into account that there was a 5%β€Ž chance that those who had not taken drugs tested positive (false-positive effect) and a 10%β€Ž 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.

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