Watching the weather channel, you can see the probability of it raining tomorrow. drag the term to the corresponding probability
1 answer:
Answer:
Probability:
1. probability of rain < 1/2 -------- Unlikely
2. probability of rain = 0 -------- Impossible
3. probability of rain = 1 -------- Certain
4. probability of rain > 1/2 --------- Likely
Step-by-step explanation:
Given -
Terms:
• impossible
• likely
• unlikely
• certain
Probability:
1. probability of rain < 1/2
2. probability of rain = 0
3. probability of rain = 1
4. probability of rain > 1/2
To find - Watching the weather channel, you can see the probability of it raining tomorrow. drag the term to the corresponding probability of it raining tomorrow. drag the term to the corresponding probability of it raining tomorrow.
Proof -
Probability:
1. probability of rain < 1/2 -------- Unlikely
2. probability of rain = 0 -------- Impossible
3. probability of rain = 1 -------- Certain
4. probability of rain > 1/2 --------- Likely
Reason -
- Probability is the chance that an event will occur. Weather predictions are based on probability.
- The probability of an event occurring is represented by a ratio.
A ratio is a number that is between 0 and 1 and can include 0 and 1.
- An event is impossible if it has a probability of 0.
Having 13 months in a year has the probability of 0.
- An event is certain if it has the probability of 1.
The probability that the sun will rise tomorrow morning is 1
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It might help to draw out a probability tree. Check out the diagram below. The first two branches at the top represent bags A and B. The probability of picking either bag is 1/2 assuming each bag is equally likely to be picked.
If we go with bag A, then the probability of getting blue is 3/11 since there are 3 blue out of 8+3 = 11 total. The probability of getting bag A and a blue marble is (1/2)*(3/11) = 3/22 which I've marked in the diagram as well.
If we go with bag B, then the probability of getting blue is 7/12 since there are 7 blue out of 5+7 = 12 total. The probability of getting bag B and blue is (1/2)*(7/12) = 7/24
Add up the results found getting
P(blue) = P(blue & bag A) + P(blue & bag B)
P(blue) = 3/22 + 7/24
P(blue) = 36/264 + 77/264
P(blue) = 113/264
This is shown in the diagram as well.
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Recall that conditional probability in general is defined as follows
P(A given B) = P(A and B)/P(B)
In this problem, we'll have
P(bag B given blue) = P(bag B and blue)/P(blue)
Therefore, we can say...
P(bag B given blue) = P(bag B and blue)/P(blue)
P(bag B given blue) = (7/24)/(113/264)
P(bag B given blue) = (7/24)*(264/113)
P(bag B given blue) = (7*264)/(24*113)
P(bag B given blue) = (7*24*11)/(24*113)
P(bag B given blue) = (7*11)/(113)
P(bag B given blue) = 77/113
In short, the probability of getting bag B, given the marble is blue, is 77/113.
