Exam 8: Sets and Probability

Assume that, at a certain college, $33 \%$ of all physics majors belong to ethnic minorities. Given a random sample of 10physics majors, find the probability of the indicated event. Round your answer as appropriate. -Seven or more belong to an ethnic minority.

Tell whether the statement is true or false. - $\{x \mid x$ is an even counting number between 8 and 14 $\}=\{6\}$

Tell whether the statement is true or false. - $\{x \mid x$ is a counting number greater than 34 $\}=\{34,35,36, \ldots\}$

Find the probability. -A family has five children. The probability of having a girl is $\frac{1}{2}$ . What is the probability of having 3 girls followed by 2 boys? Round the answer to the fourth decimal place.

Tell whether the statement is true or false. - $8 \in\{16,24,32,40,48\}$

Let $\mathrm{U}$ be the smallest possible universal set that includes all of the crops listed; and let $\mathrm{A}, \mathrm{K}$ , and $\mathrm{L}$ be the sets of five crops in Alabama, Arkansas, and Louisiana, respectively. Find the indicated set. - $A \cup L$

Find the probability of the given event. -A card drawn from a well-shuffled deck of 52 cards is a red ace.

Solve the problem. -The contingency table lists the cross tabulation of whether adults feel their life is exciting, routine, or dull for males and females among the adults chosen. Using the letters in the given table, find the number of respondents in the following set. $(\mathrm{E} \cup \mathrm{D}) \cap \mathrm{F}$

An experiment is conducted for which the sample space is $S$ assignment ispossible for this experiment. -

Use the given table to find the probability of the indicated event. Round your answer to the nearest thousandth. -College students were given three choices of pizza toppings and asked to choose one favorite. The following table shows the results. A randomly selected student prefers a meat topping.

Let $\mathrm{U}$ be the smallest possible universal set that includes all of the crops listed; and let $\mathrm{A}, \mathrm{K}$ , and $\mathrm{L}$ be the sets of five crops in Alabama, Arkansas, and Louisiana, respectively. Find the indicated set. - $\mathrm{A} \cap \mathrm{K} \cap \mathrm{L}$

Use a Venn diagram to answer the question. -At East Zone University (EZU) there are 683 students taking College Algebra or Calculus. 281 are taking College Algebra, 456 are taking Calculus, and 54 are taking both College Algebra and Calculus. How many are taking Algebra but not Calculus?

Use a Venn diagram to decide if the statement is true or false. - $A \cup(B \cup C)^{\prime}=\left(A \cup B^{\prime}\right) \cap\left(A \cup C^{\prime}\right)$

Assume that, at a certain college, $33 \%$ of all physics majors belong to ethnic minorities. Given a random sample of 10physics majors, find the probability of the indicated event. Round your answer as appropriate. -Only the first 2 and the last 2 belong to an ethnic minority.

For the experiment described, write the indicated event in set notation. -A die is tossed twice with the tosses recorded as an ordered pair. Represent the following event as a subset of the sample space: The sum of the tosses is eleven, and one toss is a six.

Determine whether the given events are disjoint. -Knowing Spanish and knowing Chinese

A die is rolled twice. Write the indicated event in set notation. -Th e first roll is a 6.

Suppose P(C) = .048, P(M ꓵ C) = .044, and P(M ꓴ C) = .524. Find the indicated probability. - $\mathrm{P}\left(\mathrm{M}^{\prime}\right)$

Let $U=\{q, r, s, t, u, v, w, x, y, z\} ; A=\{q, s, u, w, y\} ; B=\{q, s, y, z\} ;$ and $C=\{v, w, x, y, z\}$ . List the members of the indicated set, using set braces. - $\mathrm{A}^{\prime}$

Find the odds in favor of the indicated event. -Rolling an odd number with a fair die.