Math l.
asked • 02/23/16concept of probability
If there is chance of 25% rain on Saturday and 25% of rain on Sunday.Then how any chances that it will be rain on weekend ?
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Kenneth S. answered • 02/23/16
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(1/4)(1/4) = 1/16 = 0.0625
Raphael D.
1/16 would be the chance of rain on both Saturday and Sunday. Bat any rain on any of these two days is considered as "rain on weekend" - and that chance is 25%.
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02/23/16
Raphael D.
Not always you have to add probabilities, or multiply, or perform any transformations on them ...
This problem is very characteristic: you have to catch the essence of the question.
You may approach to the problem in some other way ...
look: there is 3 chances out of 4 that there is no rain on Saturday.
and, 3 chances out of 4 the no rain on Sunday.
So, in total, there are 6 chances out of 8 that no rain on both Saturday and Sandy, that is, ON WEEKEND.
If u have 6/8 chance of having no rain, then obviously, 2/8 is the chance of raining.
And 2/8 happens to be just 1/4=25%.
I wish you all a nice week:) [without rain:))]
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02/23/16
Kenneth S.
Raphael, I just posted a comment, admitting that I misread the problem.
However, the probability of rain on the weekend is 1 - 0.752 = 0.4375, i.e. 1 - p(no rain on either Sat or Sun).
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02/23/16
Math l.
I didn't understand yet. Please explain it. I am very poor at Math :((
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02/23/16
Kenneth S.
Okay...let's make a "probability tree" by starting at the middle of the left side of a page
make a line about 2 " long going upward at 45 degrees, and from the same point another line going downward at 45 degrees (from the horizontal). This makes a sideways V shape. This will represent the two choices for SATURDAY. The upper line is RAIN, so label it with that word and also 0.25, the probability of rain on Saturday.
Now label the other line NO RAIN and also its probability 0.75. This describes both possibilities for Saturday.
Now go back to the right end of the RAIN, and from that end point make another sideways V going to the right; the upper part is labeled RAIN, 0.25 and the lower part is labeled NO RAIN, 0.75--this is the set of possibilities for SUNDAY, associated with the RAIN-ON-SATURDAY.
Now go back to the right end of the NO RAIN (Saturday), and from that end point make another sideways V going to the right; the upper part is labeled RAIN, 0.25 and the lower part is labeled NO RAIN, 0.75--this is the set of possibilities for SUNDAY, associated with the NO-RAIN-ON-SATURDAY.
In the resulting figure you start at one leftmost point, and have four distinct paths, representing combinations of rain or not, for Saturday & Sunday. Each path ending at the right is a probability if one event followed by another (Sat, then Sun). The net probabilities are the PRODUCT of both probabilities written on the individual lines that make the path.
For example, the topmost 2-day path is RAIN SAT(.025), RAIN SUN (0.25); write this product (0.0625) = probability of rain on BOTH days.
The middle two paths represent NO RAIN SAT, RAIN SUN = 0.75(0.25) = 0.1875
and NO RAIN SAT, RAIN SUN = 0.25(0.75) = 0.1875
The bottom path represents NO RAIN SAT, NO RAIN SUN = 0.75(0.75) = 0.5625
Observe that the sum of the four above probabilities = 1 exactly.
Adding the top three of the above probabilities gives the probability of rain on Sat or Sun or both = 0.4375.
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02/23/16
Math l.
lower part is labeled NO RAIN, 0.75....How this value 0.75 come ?
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02/24/16
Math l.
Is it possible you explain through diagram ?
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02/24/16
Kenneth S.
if prob. of rain is 0.25, then prob. of No Rain has to be 0.75
sorry, I described the diagram. go through my narrative carefully, perhaps with a helper, & you'll find that I have described it. i don't know how to do a diagram on this 'computer platform (Wyzant)'
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02/24/16
Math l.
How you know the prob of no rain is 0.75 ?
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02/24/16
Kenneth S.
Come on! Either it rains or it doesn't. The sum of the two probabilities of these two mutually exclusive events must equal 1. END OF DISCUSSION.
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02/24/16
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Kenneth S.
02/23/16