Sue goes through 4 sets of traffic lights each morning to work. there is a 5/8 chance that she will be caught by each of the lights. if she is stopped by 3 or more of the lighs then she is late for work. what is the probability that she will be late?

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Answer 1 · 2016-01-25T15:19:06

In other words: if she has #3or#4 red lights, she will be late.

If there is an AND...AND situation we MULTIPLY the chances

#P(rrrr)=5/8*5/8*5/8*5/8=0.1526#

#P(rrrg)=5/8*5/8*5/8*3/8=0.0916#

Since the green light may be anywhere in the sequence (with the same probability) we may multiply the chance of just one green light by 4:

#P(3r+1g)=4*0.0916=0.3662#

So here we have 5 possibilities of coming late.
This is an EITHER...OR situation so we ADD probabilities:

#P(late)=0.1526+0.3662=0.5188~~52%#