Tree diagrams without replacement Probability of two or

Tree diagrams without replacement

Probability of two or more events Could make a list Could draw up a table Tree Diagrams 1 st Throw H T 2 nd Throw OUTCOMES P(Outcome) H, H P(H, H)=1/2 x 1/2=1/4 H, T P(H, T)=1/2 x 1/2=1/4 T, H P(T, H)=1/2 x 1/2=1/4 T, T P(T, T)=1/2 x 1/2=1/4 1/2 Total P(all outcomes) = 1

7 Red 3 Blue. Pick 2, without replacement. a) p(R, R) b) p(B, B) c) p(One of each) OUTCOMES 2 nd event 1 st event P(Outcome) 6/9 R, R 3/9 R, B P(R, B)=21/90 7/9 B, R P(B, R)=21/90 P(R, R)=42/90 7/10 3/10 2/9 B, B P(B, B)=6/90 Total P(all outcomes) = 1

Probability Trees Example 1 A bag contains 6 red beads and 4 blues. 2 beads are picked at random without replacement. (i) Draw a probability tree diagram to show this information (ii) Calculate the probability of selecting both red beads (iii) Calculate the probability of picking one of each colour.

Example 1 Probability Trees A bag contains 6 red beads and 4 blues. 2 beads are picked at random without replacement. (i) Draw a probability tree diagram to show this information (ii) Calculate the probability of selecting both red beads (iii) Calculate the probability of picking one of each colour. 1 st Pick 2 nd Pick R R B B R B

Example 1 Probability Trees A bag contains 6 red beads and 4 blues. 2 beads are picked at random without replacement. (i) Draw a probability tree diagram to show this information (ii) Calculate the probability of selecting both red beads (iii) Calculate the probability of picking one of each colour. 1 st Pick ? ? 2 nd Pick ? R ? B ? R B To Part (ii)

Example 1 Probability Trees A bag contains 6 red beads and 4 blues. 2 beads are picked at random without replacement. (i) Draw a probability tree diagram to show this information (ii) Calculate the probability of selecting both red beads (iii) Calculate the probability of picking one of each colour. 1 st Pick 2 nd Pick R R B B R B

Example 1 Probability Trees A bag contains 6 red beads and 4 blues. 2 beads are picked at random without replacement. (i) Draw a probability tree diagram to show this information (ii) Calculate the probability of selecting both red beads (iii) Calculate the probability of picking one of each colour. 1 st Pick 2 nd Pick R R B B R B

Probability Trees Question 1 A bag contains 7 red beads and 3 blues. 2 beads are picked at random without replacement. (i) Draw a probability tree diagram to show this information (ii) Calculate the probability of selecting both red beads (iii) Calculate the probability of picking one of each colour.

Question 1 Probability Trees A bag contains 7 red beads and 3 blues. 2 beads are picked at random without replacement. (i) Draw a probability tree diagram to show this information (ii) Calculate the probability of selecting both red beads (iii) Calculate the probability of picking one of each colour. 1 st Pick ? ? 2 nd Pick ? R ? B ? R B To Part (ii)

Question 1 Probability Trees A bag contains 7 red beads and 3 blues. 2 beads are picked at random without replacement. (i) Draw a probability tree diagram to show this information (ii) Calculate the probability of selecting both red beads (iii) Calculate the probability of picking one of each colour. 1 st Pick 2 nd Pick R R B B R B To Part (iii)

Question 1 Probability Trees A bag contains 7 red beads and 3 blues. 2 beads are picked at random without replacement. (i) Draw a probability tree diagram to show this information (ii) Calculate the probability of selecting both red beads (iii) Calculate the probability of picking one of each colour. 1 st Pick 2 nd Pick R R B B R B

Probability Trees Question 2 A bag contains 4 yellow beads and 3 blues. 2 beads are picked at random without replacement. (i) Draw a probability tree diagram to show this information (ii) Calculate the probability that both beads selected will be blue (iii) Calculate the probability of picking one of each colour.

Solution 2 Probability Trees A bag contains 4 yellow beads and 3 blues. 2 beads are picked at random without replacement. (i) Draw a probability tree diagram to show this information (ii) Calculate the probability that both beads selected will be blue (iii) Calculate the probability of picking one of each colour. 1 st Game 2 nd Game Y Y B B Y B

Question 3 Probability Trees The probability that Stuart wins a game of darts against Rose is 0. 7. They play two games. (i) Copy & complete the probability tree diagram shown below (ii) Calculate the probability Rose winning both games (iii) Calculate the probability of the final result being a draw. 1 st Game S R 2 nd Game S R

Solutions 3 Probability Trees The probability that Stuart wins a game of darts against Rose is 0. 7. They play two games. (i) Copy & complete the probability tree diagram shown below (ii) Calculate the probability Rose winning both games (iii) Calculate the probability of the final result being a draw. 1 st Game S R 2 nd Game S R