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QUESTIONS: 2014; 3d 2013; 1a 2013; 1b probability trees A = x B A’ A.B = AB B’ B B’ A + A’ B+ B’ B B’ A+A’ = 1 AB+AB’ = A Probability trees show a sequence of two or more events and the probabilities assciated with these events A A’ AB+AB’+A’B+A’B’ = 1 for instance Each individual set of branches, (associated with an event and it’s comlementary event(s)) has a total probability of 1. For example the sum of the event A, and its complementary event A’, is 1. Multiply along the branches to get the probability of the intersection of events. For example, A.B= AB. Add between the branches to get the probability of the union of events. B+ B’ + B + B’ A research scientist plants plants 11 seeds in Plot A and 9 seeds in Plot B. The probability that a seed germinates in Plot A is 0.7 and in Plot B is 0.8. Find the probability that a seed chosen at random germinates. All probabilities possible from the intersection of events , indicated at the far right of the probability tree, will equal a sum of 1. For example, the intersection of events A or A’ and B or B’ give the proabilities of AB, AB’, A’B and A’B’ will add together to give a sum of 1. The sum of the probability of the intersection of events occuring, is equal to the probability of the event that happened initially. For example, AB+AB’ =A. practice Question Solve A research scientist plants plants 11 seeds in Plot A and 9 seeds in Plot B. The probability that a seed germinates in Plot A is 0.7 and in Plot B is 0.8. Find the probability that a seed chosen at random germinates. Step One Step Two Establish variables and their relationship and form tree Find the required probabilities Variables variable 1: Plots (A or B) variable 2: Germinate (germinate or not) GERMINATE Form probability tree PLOT A Calculate probabilities of the intersection of events 9/20 0.3 NOT = 0.165 GERMINATE PLOT A GERMINATE = 0.27 PLOT B NOT GERMINATE = 0.18 0.4 GERMINATE 11/20 GERMINATE = 0.385 0.6 9/20 NOT GERMINATE PLOT B Add probabilities 11/20 0.7 P(PLOT A GERMINATE)= PLOT A . GERMINATE = 11/20 . 0.7 = 0.385 NOT GERMINATE P(PLOT A NOT GERMINATE)= PLOT A . NOT GERMINATE = 11/20 . 0.3 = 0.165 0.7 GERMINATE P(PLOT B GERMINATE)= PLOT B . GERMINATE = 9/20 . 0.6 = 0.27 0.3 NOT GERMINATE P(PLOT B NOT GERMINATE)= PLOT B . NOT GERMINATE = 9/20 . 0.4 = 0.18 0.6 GERMINATE 0.4 NOT GERMINATE PLOT A PLOT B studytime.co.nz facebook.com/studytimenewzealand Probability that a seed chosen at random germinates P(SEED GERMINATES)= 0.385 + 0.27 = 0.655 = 0.655 0.7 11/20 PLOT A 0.3 0.6 9/20 PLOT B 0.4 GERMINATE = 0.385 NOT = 0.165 GERMINATE GERMINATE = 0.27 NOT GERMINATE = 0.18