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Exam 12: From Randomness to Probability

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Question 21

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Consider a game that consists of dealing out a hand of two random cards from a deck of four cards.The deck contains the Ace of Spades (As) ,the Ace of Hearts (Ah) ,the King of Spades (Ks) and the 9 of Hearts (9h) .What is the probability that you have at most one Ace?

A) 1/6
B) 2/6
C) 3/6
D) 4/6
E) 5/6

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Question 22

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A survey of senior citizens at a doctor's office shows that 45% take blood pressure-lowering medication,41% take cholesterol-lowering medication,and 14% take both medications.What is the probability that a senior citizen takes either blood pressure-lowering or cholesterol-lowering medication?

A) 0.18
B) 0.72
C) 0.00
D) 1.00
E) 0.86

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Question 23

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An auto insurance company was interested in investigating accident rates for drivers in different age groups.The following table was based on a random sample of drivers and classifies drivers by age group and accident rate. Age Group $\begin{array} { | c | c | c | c | } \hline \begin{array} { c } \text { Number of accidents } \\\text { in past 3 years }\end{array} & \text { Under 25 } & 25 - 45 & \text { Over 45 } \\\hline 0 & 0.124 & 0.194 & 0.386 \\\hline 1 & 0.079 & 0.071 & 0.080 \\\hline > 1 & 0.030 & 0.019 & 0.017 \\\hline\end{array}$ Suppose one of these people is selected at random.Compute the probability that the person has had more than one accident in the past three years.

Many stores run "secret sales": Shoppers receive cards that determine how large a discount they get,but the percentage is revealed by scratching off that black stuff only after the purchase has been totaled at the cash register.The store is required to reveal (in the fine print) the distribution of discounts available.Determine whether the following probability assignment is legitimate. Probability of ... $\begin{array} { l | l | l | l } 10 \% \text { off } & 20 \% \text { off } & 30 \% \text { off } & 50 \% \text { off } \\\hline 0.05 & 0.30 & 0.45 & 0.10\end{array}$

Roll two fair 6-sided dice; record the smaller number.

A consumer organization estimates that 35% of the households in a particular community have one television set,36% have two sets,and 24% have three or more sets.What is the probability that a household chosen at random has no television sets?

Roll a fair 6-sided die; record the number.

Toss a fair coin five times; record the number of heads.

In a survey of women who were asked to name their favorite colour,16% said blue,19% said red,19% said green,12% said yellow,and 11% said black.If you pick a survey participant at random,what is the probability that she named a colour different from the aforementioned colours?

Consider a game that consists of dealing out a hand of two random cards from a deck of four cards.The deck contains the Ace of Spades (As) ,the Ace of Hearts (Ah) ,the King of Spades (Ks) and the 9 of Hearts (9h) .What is the probability that you have at least one Ace?

The following contingency table provides a joint frequency distribution for a group of retired people by career and age at retirement. Age at Retirement $\begin{array} { | c | c | c | c | c | c | } \hline \text { Career } & 50 - 55 & 56 - 60 & 61 - 65 & \text { Over 65 } & \text { Total } \\\hline \text { Attorney } & 12 & 44 & 73 & 43 & 172 \\\hline \begin{array} { c } \text { College } \\\text { Professor }\end{array} & 9 & 45 & 71 & 33 & 158 \\\hline \text { Secretary } & 21 & 45 & 63 & 49 & 178 \\\hline \text { Store Clerk } & 18 & 44 & 70 & 50 & 182 \\\hline \text { Total } & 60 & 178 & 277 & 175 & 690 \\\hline\end{array}$ Suppose one of these people is selected at random.Compute the probability that the person selected was an attorney who retired between 61 and 65.

The plastic arrow on a spinner for a child's game stops rotating to point at one of four colours that will determine what happens next.Determine whether the following probability assignment is legitimate. Probability of ... $\begin{array} { c | c | c | c } \text { Red } & \text { Yellow } & \text { Green } & \text { Blue } \\\hline 0.70 & 0.10 & 0.10 & 0.20\end{array}$

Melissa is looking for the perfect man.She claims that of the men at her college,36% are smart,26% are funny,and 13% are both smart and funny.If Melissa is right,what is the probability that a man chosen at random from her college is neither funny nor smart?

According to a survey in one U.S.city,49% of women between the ages and 25 of 35 are married,47% are working full time,and 21% are married and working full time.If a woman between the ages of 25 and 35 is picked at random from the city,what is the probability that she is working full time or married but not both?

Roll two fair 6-sided dice; record the positive difference.

The plastic arrow on a spinner for a child's game stops rotating to point at one of four colours that will determine what happens next.Determine whether the following probability assignment is legitimate. Probability of ... $\begin{array} { c | c | c | c } \text { Red } & \text { Yellow } & \text { Green } & \text { Blue } \\\hline 0.60 & 0.10 & 0.10 & 0.10\end{array}$

According to a survey conducted by an environmental organization,the probability that an eligible voter cares strongly about environmental issues is 0.57,the probability that an eligible voter votes regularly is 0.46 and the probability that an eligible voter both votes regularly and care strongly about environmental issues is 0.28.If an eligible voter is selected at random what is the probability that the person cares strongly about environmental issues but does not vote regularly?

The following contingency table provides a joint frequency distribution for a group of retired people by career and age at retirement. Age at Retirement $\begin{array} { | c | c | c | c | c | c | } \hline \text { Career } & 50 - 55 & 56 - 60 & 61 - 65 & \text { Over 65 } & \text { Total } \\\hline \text { Attorney } & 11 & 46 & 97 & 39 & 193 \\\hline \begin{array} { c } \text { College } \\\text { Professor }\end{array} & 9 & 37 & 90 & 48 & 184 \\\hline \text { Secretary } & 21 & 45 & 63 & 49 & 178 \\\hline \text { Store Clerk } & 18 & 44 & 70 & 50 & 182 \\\hline \text { Total } & 59 & 172 & 320 & 186 & 737 \\\hline\end{array}$ Find the probability that the person was a secretary or retired before the age of 61.

Roll a fair 6-sided die and record the number.Then flip a fair coin and record whether it comes up heads or tails.

Consider a game that consists of dealing out a hand of two random cards from a deck of four cards.The deck contains the Ace of Spades (As) ,the Ace of Hearts (Ah) ,the King of Spades (Ks) and the 9 of Hearts (9h) .Aces count as 1 or 11.Kings count as 10.You are interested in the total count of the two cards,with a maximum count of 21 (that is,AsAh = 12) .