Question

1)Make an area model(Table) or a tree diagram to model all the possible combinations in this situation. 2)What is the theoretical probability that left will add a scarf and boots(tall or short) to her outfit 3) Leave your solution as a fraction

Answer 1

Answer:

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)