Suppose traffic engineers have coordinated the timing of two traffic lights to encourage a run of green lights. In particular, the timing was designed so that with probability 0.75 a driver will find the second light to have the same color as the first, P[G2|G1] = 3/4 and P[G2|R1] = 1/4.

Assuming the first light is equally likely to be red or green, P[Gi] = 1/2.

a. Draw a tree diagram.

b. Find P[G2] and P[G1|G2].

Zahra was given two data sets, one without an outlier and one with an outlier. data without an outlier: 15, 19, 22, 26, 29 data with an outlier: 15, 19, 22, 26, 29, 81

Identify an equation in point slope form for the line perpendicular to y=3x+5 that passes through (4,-1)

In a sample of 2023 u.s. adults, 373 said franklin roosevelt was the best president since world war ii. two u.s. adults are selected at random from the population of all u.s. adults without replacement. assuming the sample is representative of all u.s. adults, complete parts (a) through (d). (a) find the probability that both adults say franklin roosevelt was the best president since world war ii. the probability that both adults say franklin roosevelt was the best president since world war ii is (round to three decimal places as needed.) (b) find the probability that neither adult says franklin roosevelt was the best president since world war ii. the probability that neither adult says franklin roosevelt was the best president since world war ii is (round to three decimal places as needed.) (c) find the probability that at least one of the two adults says franklin roosevelt was the best president since world war ii. the probability that at least one of the two adults says franklin roosevelt was the best president since world war ii is (round to three decimal places as needed.) (d) which of the events can be considered unusual? explain. select all that apply. the event in part left parenthesis a right parenthesis is unusual because its probability is less than or equal to 0.05. the event in part (b) is unusual because its probability is less than or equal to 0.05. none of these events are unusual. the event in part (c) is unusual because its probability is less than or equal to 0.05.