SOLUTION: Three are three traffic lights along the route that Ama rides from school to her home. The three lights operate independently. The probability that any one of the lights is green i

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Question 1011823: Three are three traffic lights along the route that Ama rides from school to her home. The three lights operate independently. The probability that any one of the lights is green is 0.4 and the probability that it is not green is 0.6. Estimate the probability that these lights will all be green on Ama's way home from school.
Found 2 solutions by Fombitz, Theo:
Answer by Fombitz(32388) About Me  (Show Source):
Answer by Theo(13342) About Me  (Show Source):
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.4 * .4 * .4 = .064
there is a 6.4% probability that all lights will be green when she encounters them.

if you think about it as percentages, and assume that she does a tally over 1000 trips to school, then you can think about it as follows:

40% of the rime the first light will be green.
that's 400 trips out of 1000.

in those 400 trips that the first light was green, the second light will be green 40% of the time for a total of .4 * 400 = 160 times.

in those 160 times that the first and second light was green, the third light will be green 40% of the time for a total of .4 * 160 = 64 times.

64 times out of a thousand = 64 / 1000 = .0064 = 6.4%.