Handling Data 7

A coin is tossed twice. Calculate the probability that both tosses show heads. Give your answer as a decimal.

A bag contains 1 red, 2 blue and 3 green counters. You take one at random, replace it, and then take a second counter at random. Explain why a tree diagram can be used to represent all possible outcomes for this problem.

A card is drawn at random from a pack of 52 playing cards. The card is then replaced and another card is drawn. Calculate the probability that both cards are aces.

A tree diagram has 2 branches at the first stage and each of these has 3 branches at the second stage. How many possible outcomes are shown at the end of the diagram?

The probability that a train arrives late on any day is 0.1. Find the probability that the train is late on two days in a row. Give your answer as a decimal.

The probability that it rains on a day is 0.3. Given that it rained yesterday, the probability that it will rain today is 0.4. What is the probability that it rains today, given that it rained yesterday?

A bag contains 4 red marbles and 6 blue marbles. A marble is taken at random, replaced, and then another marble is taken at random.

Work out the probability that both marbles are blue.

A bag contains 3 green counters and 2 yellow counters. Two counters are taken from the bag one after the other, without replacement.

Draw a tree diagram to show all the possible outcomes. Use your diagram to calculate the probability that both counters are green.

A box contains some balls. The probability that a randomly chosen ball is black is 0.2, and the probability that it is white is 0.5. The probability that it is red is unknown.

Given that the ball chosen is not black, explain how you would calculate the probability that it is white.