Question

10. Suppose we throw two fair dice. What is the probability that their sum is 9?

11. Suppose that A and B are events with A ⊂ B such that Pr(A) > 0. How many of the following statements are true? 0? 1? 2? (a) Pr(B | A) = 1, (b) Pr(A | B) = Pr(A)/Pr(B).

12. A family has two children including at least one daughter. What is the probability that they have two daughters?

13. Compute lim(1 + 1/n) ^n.

Answer 1

10.

When a die is thrown the outcome can be any of the numbers from 1 to 6. If two dice are thrown the set of outcomes that ensure the sum is 9 is {(3, 6), (6,3), (4, 5), (5, 4)}. The total number of possible outcomes is 6*6 = 36

This gives the required probability as 4/36 = 1/9

The probability of getting 9 as the sum when 2 dice are thrown is 0.11

11. 2 statements are true. (a) true. (b). true

12. 0.5 .

possible events for alteast one daughter in children = {(G,B),(G,G)}

Probability of two daughters=(number of events of two daughters in two children)/(number of events for alteast one daughter in two children)

=1/2

13. e (which is base of natural logorithm) as n tends to infinity