Just d.) 2. (4 pts each) Amanda likes to draw pictures with a friend. Amanda ten
ID: 3317120 • Letter: J
Question
Just d.)
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 time elves, and that she draws fairies only 20% of the time. Calculate the probability of her friend drawing a elf while visiting. (b) Suppose Amanda’s friend is known to be drawing Legolas (an elf), what are the chances that Amanda is drawing an elf? (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 exponentially 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.
Explanation / Answer
d. The choice of theme is indeoendent from picture to pictue. So the fact that one of the three pictures on display is a dragon doesn't affect the probabilities of the other two pictures.
So the probability that the second picture is a dragon = 0.5
and the probability that the third picture is a dragon = 0.5
So the probability that the other two pictures are also dragons = 0.5 x 0.5 = 0.25
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