Handling Data 5

A bag contains 5 blue counters and 3 red counters. Two counters are picked from the bag one after the other, without replacement. What is the probability that both counters picked are red?

The table shows the probability that each branch is followed on a probability tree diagram. | First Event | Probability | |:-----------:|:----------:| | Heads | 0.4 | | Tails | 0.6 |

What does the sum of the probabilities on the branches from any single event add up to in a tree diagram? Explain briefly.

A box contains 3 orange balls and 2 purple balls. A ball is picked at random, not replaced, then a second ball is picked at random.

Calculate the probability that: (a) Both balls are orange (b) The two balls picked are different colours

Maria chooses a marble from bag X and a marble from bag Y. In bag X there are 4 red and 6 blue marbles. In bag Y there are 3 red and 5 blue marbles.

She claims: 'Picking a blue marble from bag X and a red marble from bag Y is independent from picking a red marble from bag X and a blue marble from bag Y.' Is Maria correct? Give reasons for your answer.