Two dice are rolled. a) What is the probability that their sum is 10 or greater?
ID: 3233161 • Letter: T
Question
Two dice are rolled. a) What is the probability that their sum is 10 or greater? b) If the two dice are rolled 3 times, what is the probability that on at least one roll the sum was 10 or greater? c) How many times must the dice be rolled so that the probability of getting a 10 or greater on at least one roll is larger than 0.9? 7) Consider a probability experiment, with events A and B that have P(A) = 0.5, P(B) = 0.8. a) If this is all we know, what is the range of possible values for P(A Intersection B)? b) If P(A Intersection B) = 0.35, find P(A degree), P(B degree), P(A Union B), P((A U B)C), P(B Intersection A degree) and P(A Union B). c) Suppose Ralph goes to the grocery store, and A represents the event "Ralph buys bananas", and B represents the event "Ralph buys milk". In plain English, what do the numbers P(A Union B degree) and P((A Union B)degree) represent? 8) A cookie jar contains 10 delicious chocolate chip cookies and 12 yucky oatmeal-raisin cookies. Little Johny raids the cookie jar when mom isn't watching and grabs 6 cookies at random. a) What is the probability that lie gets no chocolate chip cookies? b) Let X be the number of chocolate chip cookies he gets. What is px (X)? c) He and his friend Lucy want to split the chocolate chip cookies. What is the probability that they can do so evenly? (assume they will not cut a cookie in half)Explanation / Answer
two dices are rolled
the total possible outcomes (sample space) = 6* 6 = 36
a) Probability of sum is 10 or greater
The possible outcomes for sum greater than equal to 10
(6,4)(5,5)(4,6)(6,5)(5,6)(6,6)
Thererfore P(sum>=10) = 6/36 = 1/6 = 0.1666667
b)
Rolling this 2 dice setup three times
Probability of at least one roll in which sum is greater or equal to 10 = 1 - (probability of sum less than 10 in all the three rolles)
Probability of sum les than 10 = 1 - 1/6 = 5/6
Probability of at least one roll in which sum is greater or equal to 10 = 1 - (5/6 * 5/6 * 5/6)
= 1 - 125 / 216
= 1 - 0.578703
= 0.42129
c)
On first time
Probability of at least one roll in which sum is greater or equal to 10 = 1 - 5/6
= 0.16667
On second time
Probability of at least one roll in which sum is greater or equal to 10 = 1 - 25/36 = 0.3055
On fourth time
Probability of at least one roll in which sum is greater or equal to 10 = 1 - 625/1296 = 0.5177
On fifth time
Probability of at least one roll in which sum is greater or equal to 10 = 1 - 3125/7776
on thirteen time
Probability of at least one roll in which sum is greater or equal to 10 = 1 - (5/6)^13
= 1 - 1220703125 / 13060694016
= 0.90653
Hence the they must be rolled for 13 times toe get Probability greater than 0.9
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