If two events are independent, then one does not interfere with the other. For example, suppose you are tossing a coin and drawing a card from a pack. The result of the coin (Heads or Tails) does not affect which card is selected. You can solve simple problems on independent events by drawing up a table of equally likely outcomes.

Independent Events

If the events A and B are independent, then P(A and B)P(A) x P(B)

1. The probability that Brenda goes shopping this afternoon is 0.2. The probability that Millie goes shopping this afternoon is 0.45. Calculate the probability that: a) Brenda and Millie both go shopping b) Brenda goes shopping and Millie does not.

2. A fair spinner has four sides numbered 1, 2, 3 and 4. It is spun twice. a) Draw up a two-way table to show the possible combinations of scores. b) Find the probability that the total score is 7. c) What is the most likely total score?

3. A bag contains two red balls and three green balls. A ball is chosen at random. It is then replaced, and a second ball is chosen. a) Work out the probability that the first ball is red. b) Work out the probability that both balls are red.

4. Tim has four green cards, with the numbers 1, 2, 3, 4 written on them. He has two red cards, with the numbers 5, 6 written on them. Tim chooses one red card and one green card at random. a) Draw up a two-way table to show the possible combined events. b) Work out the probability that the total of the two numbers on the cards is 8. c) Work out the probability that the total of the two numbers on the cards is even.

6. Greg throws a green dice and a blue dice. Both dice are normal fair dice, labelled with the numbers 1, 2, 3, 4, 5, 6. a) Write down the probability that the green dice shows a 4. b) Work out the probability that the green dice shows a 4 but the blue dice does not. c) Work out the probability that Greg throws a double 5.

7. Fahmi is playing a word game on a computer. The computer generates letters, from which she has to make a word. For each letter generated, the probability that it is a vowel is 0.3. Each letter is generated independently of the others. a) Write down the probability that the first letter is not a vowel. b) Work out the probability that the first two letters are both vowels.