## James goes to an arcade. He has one go on the Teddy Grabber. He has one go on the Penny Drop. The probability that he wins

Question

He has one go on the Teddy Grabber.
He has one go on the Penny Drop.
The probability that he wins on the Teddy Grabber is 0.2.
The probability that he wins on the Penny Drop is 0.3.
(a) Draw a tree diagram.
(b) Work out the probability that James wins on the Teddy Grabber and he also
wins on the Penny Drop.

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1 week 2021-09-10T00:35:16+00:00 1 Answer 0 views 0

In these lessons, we will learn

• how to draw probability tree diagrams for independent events (with replacement)

• how to draw probability tree diagrams for dependent events (without replacement)

What is a Probability Tree Diagram?

We can construct a probability tree diagram to help us solve some probability problems.

A probability tree diagram shows all the possible events. The first event is represented by a dot. From the dot, branches are drawn to represent all possible outcomes of the event. The probability of each outcome is written on its branch.

Example:

A bag contains 3 black balls and 5 white balls. Paul picks a ball at random from the bag and replaces it back in the bag. He mixes the balls in the bag and then picks another ball at random from the bag.

a) Construct a probability tree of the problem.

b) Calculate the probability that Paul picks:

i) two black balls

ii) a black ball in his second draw

Solution:

tree diagram

a) Check that the probabilities in the last column add up to 1.

b) i) To find the probability of getting two black balls, first locate the B branch and then follow the second B branch. Since these are independent events we can multiply the probability of each branch.

ii) There are two outcomes where the second ball can be black.

Either (B, B) or (W, B)

From the probability tree diagram, we get:

P(second ball black)

= P(B, B) or P(W, B)

= P(B, B) + P(W, B)

Step-by-step explanation: