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Exam 5: Probability

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Question 41

Multiple Choice

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A 12 -sided die can be made from a geometric solid called a dodecahedron. Assume that a fair dodecahedron is rolled. The sample space is {1,2,3,4,5,6,7,8,9,10,11,12}. Find P (Less than 4) .

A) 7 / 12
B) 1 / 4
C) 1 / 12
D) 1 / 3

E) B) and D)
F) None of the above

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Question 42

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Let E be the event that a corn crop has an infestation of ear worms, and let B be the event that a corn crop has an infestation of corn borers. Suppose that P(E) =0.27, P(B) =0.11, and P(E and B) =0.1 . Find the probability that a corn crop ha no corn borer infestation.

A) 0.73
B) 0.62
C) 0.28
D) 0.89

E) B) and D)
F) None of the above

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Question 43

Multiple Choice

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A section of an exam contains two multiple-choice questions, each with three answer choices (listed "A", "B", and "C") . Assuming the outcomes to be equally likely, find the probability (as a reduced Fraction) that at least one answer is "A". [Hint: List all the outcomes of the sample space first.]

Nanette must pass through three doors as she walks from her company's foyer to her office. Each of these doors may be locked or unlocked. Let C be the event that at least two doors are unlocked. List the outcomes of C. [Let "L" designate "locked" and "U" designate "unlocked".]

Let A and B be events with $P ( A ) = 0.9 , P ( B ) = 0.6 , \text { and } P ( A \text { and } B ) = 0.27$ . Are A and B mutually exclusive?

Nanette must pass through three doors as she walks from her company's foyer to her office. Each of these doors may be locked or unlocked. Let C be the event that at least two doors are in the same condition. List the outcomes of C. [Let "L" designate "locked" and "U" designate "unlocked".]

Nanette must pass through three doors as she walks from her company's foyer to her office. Each of these doors may be locked or unlocked. Let B be the event that exactly two doors are in the same condition. List the outcomes of B. [Let "L" designate "locked" and "U" designate "unlocked".]

Nanette must pass through three doors as she walks from her company's foyer to her office. Each of these doors may be locked or unlocked. List the outcomes of the sample space.

A Karate club consists of 52 persons holding a black belt (highest rating) , 69 persons holding a brown belt (middle rating) , and 77 persons holding a purple belt (lowest rating) . What is the Probability that a randomly-selected club member holds a brown belt or a purple belt?

A section of an exam contains two multiple-choice questions, each with three answer choices (listed "A", "B", and "C") . Assuming the outcomes to be equally likely, find the probability (as a reduced Fraction) that both answers are "C". [Hint: List all the outcomes of the sample space first.]

Evaluate the permutation: ${ } _ { 11 } P _ { 6 }$

On a TV game show, a contestant is shown 9 products from a grocery store and is asked to choose the three least-expensive items in the set, and then correctly arrange these three items in order of Price. In how many ways can the contestant choose the three items?

So far this season, the university's football team has executed 146 running plays, 167 passing plays, and 22 "trick" plays. What is the probability that the team will execute a passing play?

A geneticist is studying two genes. Each gene can be either dominant or recessive. A sample of 100 individuals is categorized as follows. $\begin{array} { c c c } & \text { Gene 2 } & \text { Gene 2 } \\\text { Dominant } & \text { Recessive } \\\text { Gene 1 Dominant } & 12 & 18 \\\text { Gene 1 Recessive } & 28 & 42\end{array}$ What is the probability that in a randomly-sampled individual, gene 2 is dominant?

A poll was taken of 14,360 working adults aged 40-70 to determine their level of education. The participants were classified by sex and by level of education. The results were as follows. $\begin{array} { c c c c } \hline \text { Education Level } & \text { Male } & \text { Female } & \text { Total } \\\hline \text { High School or Less } & 3,092 & 2,294 & 5,386 \\\text { Bachelor's Degree } & 3,607 & 4,247 & 7,854 \\\text { Master's Degree } & 584 & 437 & 1,021 \\\text { Ph.D. } & 50 & 49 & 99 \\\hline \text { Total } & 7,333 & 7,027 & 14,360\end{array}$ A person is selected at random. Compute the probability that the person is male or has a Ph.D.

A committee consists of 10 women and 7 men. Three members are chosen as officers. What is the probability that all three officers are women?

The probability that a certain make of car will need repairs in the first six months is 0.4. A dealer sells seven such cars. What is the probability that at least one of them will require repairs in the first Six months?

A study suggests that 14.7% of all four-digit personal identification numbers, or PIN codes, have a repeating-digits format such as 2525. Assuming this to be true, if the PIN codes of four people are Selected at random, what is the probability that at least one of them will have repeating digits?

A Karate club consists of 54 persons holding a black belt (highest rating) , 64 persons holding a brown belt (middle rating) , and 79 persons holding a purple belt (lowest rating) . What is the Probability that a randomly-selected club member holds a black belt?

William and Mary are going bowling. The probability that Mary scores more than 175 is 0.6, and the probability that William scores more than 175 is 0.7. Their scores are independent. a. Find the probability that both score more than 175 . b. Given that William scores more than 175 , the probability that Mary scores higher than William is 0.4. Find the probability that William scores more than 175 and Mary scores higher than William.