True False True False True False Starter – True or False You are equally likely to get a heads or tails when flipping a fair coin True False You are more likely to get an even number when rolling a fair die The probability of picking a red card is 2/3 True The probability of landing on a 1 on the spinner is 1/4 2 5 4 3 False The probability of not picking a black card is 4/6 True The probability of choosing an ‘A’ from is 2/10 False

Answer: P(Black or Green) = 4 9 + 3 9 = 7 9 The OR rule Example 1 Rebecca has nine coloured beads in a bag. Four of the beads are black, two are red and the rest are green. She removes a bead at random from the bag and notes the colour. What is the probability she chooses a black bead or a green bead ? Answer: P(Black or Green) = 4 9 + 3 9 = 7 9 The OR rule For mutually exclusive events; P( A or B) = P(A) + P(B)

Answer: P(Black and black) = 4 9 × 4 9 = 16 81 The AND rule Example 1 Rebecca has nine coloured beads in a bag. Four of the beads are black, 2 are red and the rest are green. She removes a bead at random from the bag and notes the colour before replacing it. She then chooses a second bead. What is the probability she chooses a black bead both times? Answer: P(Black and black) = 4 9 × 4 9 = 16 81 The AND rule For independent events; P( A and B) = P(A) x P(B)

Ends of first and second level branches show the different outcomes. Probability Trees The probabilities for each event are shown along the arm of each branch and they sum to 1. Ends of first and second level branches show the different outcomes.

Rebecca has nine coloured beads in a bag Rebecca has nine coloured beads in a bag. Four of the beads are black and the rest are green. She removes a bead at random from the bag and notes the colour before replacing it. She then chooses a second bead. Draw a tree diagram showing all possible outcomes. Calculate the probability that Rebecca chooses: (i) 2 green beads (ii) Two different coloured beads. First Choice Second Choice black black green black green green

Complete the worksheet.

Extension There are 4 blackcurrant sweets, 3 apple sweets and 4 strawberry sweets in a bowl. I pick two sweets (And do not replace them). What is the probability that I pick two sweets of the same flavour?