Probability

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beck15

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A getaway driver needs to get to a distant city and wishes to arrive as quickly as possible. She considers taking the shortest route – through the mountains. It is winter, there is some possibility that it will snow hard enough to block the road; she will not get through if it snows and the mountain road is blocked. She estimates the probability of it snowing as 0.2 and the probability of the road staying open given it snows as 0.6. What is the probability that she will get through if she takes the mountain road?
 

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Write down all the probabilities that are given and which one that you want to find. Then try to connect all or some of them. Please post back with your work.
 
Steven G said:
Write down all the probabilities that are given and which one that you want to find. Then try to connect all or some of them. Please post back with your work.
Click to expand...
Chance of snow: 0.2
Chance of it staying open if it snows = 0.6
Chance of it not snowing = 0.8
Chance of closing if it snows = 0.4
P = p(0.2 + 0.6) x (0.8 + 0.4)
0.2 + 0.6 = 0.8
0.8 + 0.4 = 0.12
0.8 x 0.12 = 0.96
P = 0.96
 
You may or not be correct. Why can't I tell? You failed to define P.

Also, 0.8 > 0.12, so how can 0.8 + 0.4 = 0.12?
0.8*0.12 is NOT 0.96. You can't multiply two positive numbers both less that 1 and the result be larger than both numbers!
 
Virtually all of probability is summed up in

[math]\text {A probability is a real number in the interval } [0,\ 1].\\ \text {A is certain} \iff \text {P(A)} = 1.\\ \text {A is impossible} \implies \text {P(A)} = 0.\\ \text {P(A or B)} = \text {P(A)} + \text {P(B)} - \text {P(A and B)}.\\ \text {A and B are mutually exclusive} \iff \text {P(A and B)} = 0.\\ \text {P(A)} = 0 \implies \text {P(B given A) is not defined.}\\ \text {If P(A)} > 0 \implies \text {P(B given A)} = \text {P(A and B)} \div \text {P(A)}.\\ \text {A and B are independent} \iff \text {P(A and B)} = \text {P(A)} * \text {P(B)}.[/math]
What are A and B in this problem?
 
JeffM said:
Virtually all of probability is summed up in

[math]\text {A probability is a real number in the interval } [0,\ 1].\\ \text {A is certain} \iff \text {P(A)} = 1.\\ \text {A is impossible} \implies \text {P(A)} = 0.\\ \text {P(A or B)} = \text {P(A)} + \text {P(B)} - \text {P(A and B)}.\\ \text {A and B are mutually exclusive} \iff \text {P(A and B)} = 0.\\ \text {P(A)} = 0 \implies \text {P(B given A) is not defined.}\\ \text {If P(A)} > 0 \implies \text {P(B given A)} = \text {P(A and B)} \div \text {P(A)}.\\ \text {A and B are independent} \iff \text {P(A and B)} = \text {P(A)} * \text {P(B)}.[/math]
What are A and B in this problem?
Click to expand...
I wish that I had this information when I studied probability!!
 
beck15 said:
Chance of snow: 0.2
Chance of it staying open if it snows = 0.6
Chance of it not snowing = 0.8
Chance of closing if it snows = 0.4
P = p(0.2 + 0.6) x (0.8 + 0.4)
0.2 + 0.6 = 0.8
0.8 + 0.4 = 0.12
0.8 x 0.12 = 0.96
P = 0.96
Click to expand...
It was a good idea to describe the first 4 values. Can you add comments for the remaining lines? This might help you figure out where you gone wrong.
 
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