Question

8. Two six-sided dice are rolled. Show work, including conditional formula set-up to find the probability that the sum of both sides up is 10 given that we know that the sum is greater than 6. 9. It is known that toddlers pick red-colored toys more often than other colors (70% of the time). Second on the list is bright yellow (20%) and all other colors together with 10% of the times. Three bowls with cookies are left at a play room. The red bowl has 10 chocolate chip cookies and 5 oatmeal cookies. The bright yellow bowl has 20 chocolate chip cookies and 10 oatmeal cookies. The last bowl has 5 chocolate chip cookies and 5 oatmeal cookies. A toddler is left alone is the room, then asked to come out. The toddler has a chocolate cookies in his/her hand. What is the probability that the chocolate cookie came from the bright yellow bowl? MUST show all work. 10. Farmers around the world (probably except in the USA and Canada) predict the weather with some accuracy. A certain farmer in Latin America correctly predicts rain 90% of the times. When it does not rain, however, the farmer predicts rain 20% of the times. With the given information, what is the probability it rains given that the farmer predicted rain?

Answer 1

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8. P(sum=10|sum>6) = ?
So,
Sum is 7 in {3,4},{4,3},{5,2},{2,5},{6,1},{1,6} = 6 cases
Sum is 8 in {4,4},{5,3},{3,5},{2,6},{6,2} = 5 cases
Sum is 9 in {4,5},{5,4},{3,6},{6,3} = 4 cases
Sum is 10 in {4,6},{6,4},{5,5} = 3 cases
Sum is 11 in {6,5},{5,6} = 2 cases
Sum is 12 in {6,6} = 1 cases
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so sum>6 is 6+5+4+3+2+1 = 21

So, out of these 21 cases, 3 cases have sum equal to 10.
Hence, P(sum=10|sum>6) = sum is greater than 6 and is 10 / total cases where sum >6
= 3/21
= 1/7