ONLY ANSWER QUESTION 2.e 2. (4 pts each) Amanda likes to draw pictures with a fr
ID: 3313124 • Letter: O
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ONLY ANSWER QUESTION 2.e
2. (4 pts each) Amanda likes to draw pictures with a friend. Amanda tends to draw pictures in one of three themes: dragons, elves, or fairies. If Amanda decides to draw a picture in one theme, her friend is twice as likely to draw a picture of the same theme than to draw a picture in either of the other two themes. If her friend decides to draw something different, she is equally likely to pick either of the remaining two themes (a) Suppose that half the time Amanda draws dragons, 30% of the tine elves, and that she draws fairies only 20% of the time. Calculate the probability of her friend drawing a elf while visiting Suppose Amanda's friend is known to be drawing Legolas (an elf), what are the chances that Amanda is drawing an elf? (b) (c) The time it takes Amanda to draw a dragon is exponentially distributed with a mean of 30 minutes. The time her friend takes to draw a landscape is also distributed, but with a mean of 25 minutes. When one finishes, the other one quits so they can go watch T.V. together. What is the expected amount of time until they are ready to watch T.V.? (d) Amanda draws a set of three pictures. Walking through the room, you notice that one of them is a picture of a dragon. What are the chances that the other two are also dragons? Here assume the choice of theme is independent from picture to picture (e) When you ask about the picture, Amanda tells you it is Smaug from The Hobbit, and that it was first picture she drew that day. Does this new information change the chances that the other two pictures are dragons? If so, exactly how?Explanation / Answer
2e. This new information does change the chances of the other two being dragons
The difference between question parts d and e is that in d, we do not know whether the picture we see is the 1st, 2nd or 3rd one that Amanda has drawn. Hence, when she tells us that the picture we see is the first one she drew, we know her starting point was a dragon. So, the probability of the next 2 being dragons too is a straightforward calculation according to her friend's and her propensities.
= P(2nd and 3rd being dragons GIVEN 1st is dragon)
In the part d, we don't know whether the picture we see is the 1st/2nd/3rd one that she has drawn. Hence, the probability of all 3 pictures being dragons equals
= P(picture seen is 1st)*P(2nd and 3rd being dragons GIVEN 1st is dragon)
+ P(picture seen is 2nd)*P(1st and 3rd being dragons GIVEN 2nd is dragon)
+ P(picture seen is 3rd)*P(1st and 2nd being dragons GIVEN 3rd is dragon)
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