The route used by a certain motorist in commuting to work contains two intersections with traffic signals. The probability that he must stop at the first signal is 0.5 and the probability that he must stop at the second signal is 0.4, and the probability that he must stop at least one of the two signals is 0.6. Let S? be the event that he must stop at first signal and S? be the event that he must stop at the second signal. What is the probability that he must stop a. at both the signals? b. at exactly one signal? c. at the second signal given that he has not stopped at the first signal
Added by Sharon B.
Close
Step 1
We are given the probability of stopping at each signal individually, as well as the probability of stopping at at least one of the signals. We can use the formula for the probability of the union of two events to find the probability of stopping at both Show moreā¦
Show all steps
Your feedback will help us improve your experience
Adi S and 57 other Intro Stats / AP Statistics educators are ready to help you.
Ask a new question
Labs
Want to see this concept in action?
Explore this concept interactively to see how it behaves as you change inputs.
Key Concepts
Recommended Videos
'The route used by certain motorist in commuting to work contains two intersections with traffic signals. The probability that he must stop at the first signal is 0.45_ the analogous probability for the second signal is 0.5 and the probability that he must stop at at east one of the two signals is 0.8 (a) What is the probability that he must stop at both signals? What the probability that he must stop at the first signal but not at the second one? (c) What Is the probability that he must stop at exactly one signal?'
Sri K.
The route used by a driver in commuting to work contains two intersections with traffic signals. The probability that he 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 one or more 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?
Probability
Axioms, Interpretations, and Properties of Probability
The route used by a certain motorist in commuting to work contains two distant intersections with long traffic signals. Let A be the event that she must stop at the first signal, and let B be the event that she must stop at the second signal. (a) If P(A āŖ B) = 0.80, P(A) = 2P(B), and P(A ā© B) = 0.20, what is the probability that she must stop at the first traffic signal? (b) Suppose that P(A) = 0.30, and P(B'|A) = 0.20, what is the probability that she must stop at both traffic signals? (c) If P(A) = 0.55, P(B) = 0.45, and P(A ā© B) = 0.30, what is the probability that she does not have to stop when commuting to work at either traffic signal?
Recommended Textbooks
Elementary Statistics a Step by Step Approach
The Practice of Statistics for AP
Introductory Statistics
Transcript
Watch the video solution with this free unlock.
EMAIL
PASSWORD