help with probability?

Question

I need assistance with a probability problem related to a motorist's route that includes two intersections with traffic lights. The probability that the motorist must stop at the first signal is 0.4, and for the second signal, it is 0.5. Additionally, the probability that he must stop at least one of the two signals is 0.6. 
I am looking to find the following probabilities:
a) the probability that he must stop at both signals,
b) the probability that he must stop at the first signal but not at the second one, and 
c) the probability that he must stop at exactly one signal.
If possible, I would appreciate it if you could explain how you arrived at the answers or provide hints to help me solve these questions on my own. Thank you!

Prof. Colin Grady IV · Accepted Answer

let us call the first signal A & the second signal B
draw a venn diagram to make things clearer
qa
P[A] = 0.4, P[B] = 0.5, P[A or B] = 0.6
now P[A or B] = P[A] + P[B] - P[A & B]
or 0.6 = 0.4 + 0.5 - P[A & B]
so P[A & B] 
=  P[ stopping at both signals ]
= 0.3
qb
P[ stopping only at the 1st signal ]
= P[A] - P[A & B] 
= 0.4 - 0.3
= 0.1
qc
P[ stopping only at the 2nd signal ]
= P[B] - P[A & B]
= 0.5 - 0.3
= 0.2
we have already found P[stopping only at 1st signal]
adding the two, we get
P[stopping at only one signal]
= 0.3 + 0.2
= 0.5

Freddy Rodriguez · Answer

answer is .3 for the last part (.1 + .2) = .3

Nathanial Gulgowski · Answer

I dont know

Anonymous

help with probability?

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