#### MATH 1711

##### Midterm 2 | Spring '14| Barone
Two fair die are rolled and the numbers facing upwards are recorded. What is the possibility that the number add up to 8 hours? Show your work.

There are $4487$ words in U.S. Construction. The word "shall" occurs $191$ times and the word "states" appers $91$ times. What is ta possibility that a word randomly chosen from the constuction is neither "shall" nor "states"?

Let $E$ and $F$ be two possible event in an experiment. If $Pr(E)=.6, Pr(F)=.4$ and $Pr(E \cap F') = .5$ then find $Pr(E' \cap F)$.

Let $S$ be a simple space and $E$ and $F$ be events from the sample spaces. Suppose that $Pr(E)=.5$ and $Pr(F)=.6$ and $Pr(E \cap F) = .2$ and $Pr(E \cap F) = .2$. What is $Pr(E|F)$?

An urn contains 6 white balls and 3 green balls. A ball is selected at random and placed on a table, then another ball is selected abd placed next to the first ball.

(6 pts. each)

(a) What is the probability that both balls are green?

(b) What is the probability that both balls are green ball selected was green?

There are two urns: a white urn containing three white balls and a red ball and a red urn containing one white ball and four red balls. An experiment consists of selecting a ball at random from the white urn and then (without replacement) selecting a ball at ramdom from the urn with the same color as the first ball selected. What is the probalitity that the second bal selected is red?

(16 pts.)

A fair die is rolled seven times and the numbers facing upwards are recorded. What is the probability of rolling exactly four $3 #39;s? (10 pts.) Log in or sign up to see discussion or post a question. If$E$and$F$are independent events of a sample space$S$and$Pr(E)=.5$and$Pr(F)=.3$, then what is$Pr(E|F)$? Log in or sign up to see discussion or post a question. True or False questions. (a) A red die and a green die are rolled. Let the event$E$be "the sum of the numbers showing is 7" and let$F$be the event "the red die is a$6
(i) The events $E$ and $F$ are independent. TRUE/FALSE
(ii) The events $E$ and $F$ are not mutually exclusive. TRUE/FALSE
(b) If $s$ is an outcome of a sample space $S$ and $Pr(s) = .4$, then the odds of $S$ occurring are $2$ to $5$. TRUE/FALSE