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.

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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"?

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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 $Pr(E' \cap F)$.

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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 $Pr(E|F)$?

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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?

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

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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.)


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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.)


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If $E$ and $F$ are independent events of a sample space $S$ and $Pr(E)=.5$ and $Pr(F)=.3$, then what is $Pr(E|F)$?

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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
quot;.
      (i) The events $E$ and $F$ are independent. TRUE/FALSE
      (ii) The events $E$ and $F$ are not mutually exclusive. TRUE/FALSE

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(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

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