Conditional Probability Traffic light question

In summary, the conversation discusses a probability problem involving two consecutive stoplights, with a given probability of a red light at the first intersection and a conditional probability of a green light at the second intersection given a green light at the first. The question asks for the probability of a green light at both intersections. The conversation also mentions using a formula for conditional probability to solve the problem.
  • #1
Pure Canuck
1
0
Hey guys Me and my friend just got this question and it seems easy but i just want to make sure we are right anyway here it is:

A road has two stoplights at consecutive intersections. The prob. of a red at the first is 0.55 and the probability of a green at the second, give a green at light oine is .75

Find the prob of a green at both intersections:
Givens = (r1 = .55) (g2|g1=.75)
now i believe its simply as just r1*.75.

which is like .33

Anybody know if i did this right?

Thanks
 
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  • #2
In your problem statement:

[itex]P(r_1 )=0.55[/itex] and [itex]P(g_2 |g_1 )=0.75[/itex]

but I don't know how you got your answer because .55*.75 = .4125, though I do agree that .33 is very close to the answer, depending on how you round the decimal.
 
  • #3
Hint: http://mathworld.wolfram.com/ConditionalProbability.html" .
Just use the formula.
 
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1. What is conditional probability?

Conditional probability is the likelihood of an event occurring given that another event has already occurred. It is calculated by dividing the probability of the two events happening together by the probability of the given event.

2. How does conditional probability apply to the traffic light question?

In the traffic light question, we are given the probability of two events: the probability of the light being green and the probability of the light being red. We can use conditional probability to calculate the probability of one event (the light being green) given that the other event (the light being red) has already occurred.

3. What is the formula for conditional probability?

The formula for conditional probability is P(A|B) = P(A and B) / P(B), where P(A|B) represents the probability of event A occurring given that event B has occurred, P(A and B) represents the probability of both events occurring together, and P(B) represents the probability of event B occurring.

4. How do you solve the traffic light question using conditional probability?

To solve the traffic light question using conditional probability, we first need to determine the probability of both events occurring together. In this case, it would be the probability of the light being green and the light being red (P(G and R)). Then, we divide this by the probability of the given event (P(R)) to get the conditional probability of the light being green given that it is already red (P(G|R)).

5. What are some real-world applications of conditional probability?

Conditional probability is used in a variety of fields, such as finance, medicine, and weather forecasting. Some examples include predicting the likelihood of a stock market crash given certain economic indicators, determining the probability of a patient having a particular disease based on their symptoms, and forecasting the chances of rain given the current weather conditions.

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