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In this problem, it is said that we have two arms and we flip a fair coin.
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If the outcome is heads, then a ball from urn a is selected.
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And if the outcome is tails, then a ball from urn b is selected.
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Now, suppose that a white ball is selected, then what is the probability that the coin landed tails? so let us define a few events.
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Let h be the event that the coin landed heads.
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Let t be the event that the coin landed tails.
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And let w be the when that a white ball is selected.
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Then the probability of getting a heads, that will be the number of favorable outcomes divided by the total number of outcomes.
00:46
When we flip a coin, there are only two outcomes, heads or tails, so that's in the denominator two.
00:51
And if we want the probability of heads, the number of favorable outcomes is one because the only favorable outcome is heads.
00:58
Similarly, the probability of getting a tails will also be 1 divided by 2 because there are two outcomes heads and tails and the only favorable outcome is tails so we have 1 divided by 2 next let us determine the probability of w given h that is the probability of getting a white ball given that we get a heads so if we get a heads then it is said that a ball from urn a is selected so what we actually need to determine is the probability of drawing a white ball from urn a.
01:30
Now there are a total of five white balls in urn a, so the number of favorable outcomes is five.
01:37
And there are seven black balls as well.
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So five plus seven is 12.
01:43
So there is a total number of outcomes, 12.
01:45
So the probability will be five by 12.
01:48
And next let us find the probability of w given t.
01:51
There's the probability of getting a white ball given that the outcome is tails.
01:55
And if the outcome is tails, then a ball from arn b, selected.
01:59
So this will actually be equal to the probability of selecting a ball from r &b, a white ball from r &b.
02:06
Now r &b has three white balls, so the number of favorable outcomes is three, and there are 12 black balls...