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Oswald Hills

Feb 20, 2025

help with probability?

the route used by a motorist contains two intersections with traffic lighs. The probability that the motorist must stop at the first signal is .4., the analogous probability for the second signal is .5, and the probability that he must stop at at least one of the two signals is .6. What is the probability that he must stop:a) at both signals?b) at the first signal but not at the second one?c) at exactly one signal?if you can, please explain how you got the answers, or give me a hint to help me figure the answers out. thanks.
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let us call the first signal A & the second signal Bdraw a venn diagram to make things clearerqaP[A] = 0.4, P[B] = 0.5, P[A or B] = 0.6now 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 ]= 0.3qbP[ stopping only at the 1st signal ]= P[A] - P[A & B] = 0.4 - 0.3= 0.1qcP[ stopping only at the 2nd signal ]= P[B] - P[A & B]= 0.5 - 0.3= 0.2we have already found P[stopping only at 1st signal]adding the two, we getP[stopping at only one signal]= 0.3 + 0.2= 0.5... Show More
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