Question 1

Find the indicated probability
-A batch consists of 12 defective coils and 88 good ones. Find the probability of getting two good coils when two coils are randomly selected if the first selection is replaced before the second is made.

Accepted Answer

The probability of selecting a good coil is 88/100. Since the first selection is replaced, the probability remains the same for the second selection. Thus, the probability of selecting two good coils in a row is (88/100) * (88/100) = 0.7744.

Question 2

Find the indicated probability
-Find the probability that 3 randomly selected people all have the same birthday. Ignore leap years.

Accepted Answer

The probability that 3 randomly selected people all have the same birthday, ignoring leap years, is calculated by considering that the first person can have any birthday, the second person must have the same birthday as the first (1/365 chance), and the third must also match (1/365 chance). Thus, the probability is $1 \times \frac{1}{365} \times \frac{1}{365} = \frac{1}{365^2} \approx 0.00000751$.

Question 3

Find the indicated probability
-The table below describes the smoking habits of a group of asthma sufferers. $\begin{array}{r|cccc} 
&& \text {light}& \text {heavy}\
& \text { Nonsmoker } & \text { smoker} & \text { smoker } & \text {Total } \
\hline \text { Men } & 341 & 45 & 36 & 422 \
\text { Women } & 383 & 38 & 37 & 458 \
\text { Total } & 724 & 83 & 73 & 880
\end{array}$
If two different people are randomly selected from the 880 subjects, find the probability that they are both heavy smokers.

Accepted Answer

The answer of Find the indicated probability
-The table below describes...

Question 4

Provide a written description of the complement of the given event.
-The table below describes the smoking habits of a group of asthma sufferers. $\begin{array}{r|cccc} 
&& \text {light}& \text {heavy}\
& \text { Nonsmoker } & \text { smoker  } & \text {smoker } & \text { Total } \
\hline \text { Men } & 417 & 34 & 31 & 482 \
\text { Women } & 367 & 45 & 47 & 459 \
\text { Total } & 784 & 79 & 78 & 941
\end{array}$
If two different people are randomly selected from the 941 subjects, find the probability that they are both wome:

Accepted Answer

The complement of the event "both are women" is "at least one is not a woman". The probability of this event is 1 minus the probability of the event "both are women". The probability of the event "both are women" is:$$P(	ext{both are women}) = \frac{459}{941} 	imes \frac{458}{940} = 0.2377$$Therefore, the probability of the complement of the event "both are women" is:$$P(	ext{at least one is not a woman}) = 1 - 0.2377 = 0.7623$$

Question 5

Find the indicated probability
-Among the contestants in a competition are 42 women and 28 men. If 5 winners are randomly selected, what is the probability that they are all men?

Accepted Answer

The probability of selecting 5 men out of a total of 70 contestants (42 women + 28 men) without replacement is calculated using combinations. The probability is the number of ways to choose 5 men out of 28 divided by the number of ways to choose 5 people out of 70, which is (28C5)/(70C5) = 0.00812.

Question 6

Find the indicated probability
-A sample of 4 different calculators is randomly selected from a group containing 42 that are defective and 27 that have no defects. What is the probability that all four of the calculators selected are defective?

Accepted Answer

The answer of Find the indicated probability
-A sample of 4...

Question 7

Find the indicated probability
-You are dealt two cards successively (without replacement)from a shuffled deck of 52 playing cards. Find the probability that the first card is a King and the second card is a queen.

Accepted Answer

The probability of drawing a King first is $\frac{4}{52}$ since there are 4 Kings in a deck of 52 cards. After drawing a King, there are 51 cards left, and the probability of drawing a Queen next is $\frac{4}{51}$ since there are 4 Queens in the remaining deck. Multiplying these probabilities gives $\frac{4}{52} \times \frac{4}{51} = \frac{16}{2652} = \frac{4}{663}$.

Question 8

Find the indicated probability
-You are dealt two cards successively (without replacement)from a shuffled deck of 52 playing cards. Find the probability that both cards are black.

Accepted Answer

The probability of drawing a black card first is $\frac{26}{52}$ since half of the 52 cards are black. After drawing one black card, there are now 51 cards left in the deck, with 25 of them being black. Thus, the probability of drawing another black card is $\frac{25}{51}$. Multiplying these probabilities gives the overall probability of drawing two black cards in succession: $\frac{26}{52} \times \frac{25}{51} = \frac{1}{2} \times \frac{25}{51} = \frac{25}{102}$.

Question 9

Find the indicated probability
-In a homicide case 6 different witnesses picked the same man from a line up. The line up contained 5 men. If the identifications were made by random guesses, find the probability that all 6 witnesses would pick the same person.

Accepted Answer

The answer of Find the indicated probability
-In a homicide case...

Question 10

Provide a written description of the complement of the given event.
-Of the thirteen different women Calvin asks for a date, at least one of them accepts.

Accepted Answer

The complement of at least one woman accepting Calvin's offer is that none of the women accept his offer.

Question 11

Find the indicated probability
-A study conducted at a certain college shows that 60% of the school's graduates find a job in their chosen field within a year after graduation. Find the probability that 11 randomly selected graduates all find jobs in their chosen field within a year of graduating.

Accepted Answer

The probability that all 11 graduates find jobs in their chosen field is $0.6^{11}$ because each event (each graduate finding a job) is independent and has a probability of 0.6. Calculating $0.6^{11}$ gives approximately 0.004.

Question 12

Find the indicated probability
-A IRS auditor randomly selects 3 tax returns from 57 returns of which 6 contain errors. What is the probability that she selects none of those containing errors?

Accepted Answer

The answer of Find the indicated probability
-A IRS auditor randomly...

Question 13

Find the indicated probability
-What is the probability that 4 randomly selected people all have different birthdays?

Accepted Answer

The answer of Find the indicated probability
-What is the probability...

Question 14

Find the indicated probability
-When a pair of dice are rolled there are 36 different possible outcomes: 1-1, 1-2, ... 6-6. If a pair of dice are rolled 4 times, what is the probability of getting a sum of 7 every time?

Accepted Answer

The answer of Find the indicated probability
-When a pair of...

Question 15

Find the indicated probability
-A manufacturing process has a 70% yield, meaning that 70% of the products are acceptable and 30% are defective. If three of the products are randomly selected, find the probability that all of them are acceptable.

Accepted Answer

The probability that all three products are acceptable is found by multiplying the probability of one being acceptable (70% or 0.7) three times: $0.7 \times 0.7 \times 0.7 = 0.343$.

Question 16

Find the indicated probability
-In one town, 60% of adults have health insurance. What is the probability that 9 adults selected at random from the town all have health insurance?

Accepted Answer

The probability that one adult has health insurance is 0.6. For 9 adults, all having health insurance independently, the probability is $0.6^9 \approx 0.01$.

Question 17

Provide a written description of the complement of the given event.
-When several textbooks are returned from editing, none of the books are found to be errorless.

Accepted Answer

The complement of finding none of the books errorless is finding at least one book without errors.

Question 18

Provide a written description of the complement of the given event.
-When 10 adults are tested for high blood pressure, at least one of the results are positive.

Accepted Answer

The complement of at least one adult testing positive for high blood pressure is that none of the adults test positive for high blood pressure.

Question 19

Provide a written description of the complement of the given event.
-When 100 engines are shipped, all of them are free of defects.

Accepted Answer

The complement of all engines being free of defects is that at least one engine is defective, as it directly opposes the scenario where all engines are perfect.

Question 20

Find the indicated probability
-A bin contains 71 light bulbs of which 9 are defective. If 6 light bulbs are randomly selected from the bin with replacement, find the probability that all the bulbs selected are good ones.

Accepted Answer

Probability of selecting a good bulb = 62/71Probability of selecting 6 good bulbs = (62/71)^6 = 0.443

Quiz 4: Probability

Find the indicated probability -A batch consists of 12 defective coils and 88 good ones. Find the probability of getting two good coils when two coils are randomly selected if the first selection is replaced before the second is made.

Find the indicated probability -Find the probability that 3 randomly selected people all have the same birthday. Ignore leap years.

Find the indicated probability -Among the contestants in a competition are 42 women and 28 men. If 5 winners are randomly selected, what is the probability that they are all men?

Find the indicated probability -A sample of 4 different calculators is randomly selected from a group containing 42 that are defective and 27 that have no defects. What is the probability that all four of the calculators selected are defective?

Find the indicated probability -You are dealt two cards successively (without replacement) from a shuffled deck of 52 playing cards. Find the probability that the first card is a King and the second card is a queen.

Find the indicated probability -You are dealt two cards successively (without replacement) from a shuffled deck of 52 playing cards. Find the probability that both cards are black.

Find the indicated probability -In a homicide case 6 different witnesses picked the same man from a line up. The line up contained 5 men. If the identifications were made by random guesses, find the probability that all 6 witnesses would pick the same person.

Provide a written description of the complement of the given event. -Of the thirteen different women Calvin asks for a date, at least one of them accepts.

Find the indicated probability -A study conducted at a certain college shows that 60% of the school's graduates find a job in their chosen field within a year after graduation. Find the probability that 11 randomly selected graduates all find jobs in their chosen field within a year of graduating.

Find the indicated probability -A IRS auditor randomly selects 3 tax returns from 57 returns of which 6 contain errors. What is the probability that she selects none of those containing errors?

Find the indicated probability -What is the probability that 4 randomly selected people all have different birthdays?

Find the indicated probability -When a pair of dice are rolled there are 36 different possible outcomes: 1-1, 1-2, ... 6-6. If a pair of dice are rolled 4 times, what is the probability of getting a sum of 7 every time?

Find the indicated probability -A manufacturing process has a 70% yield, meaning that 70% of the products are acceptable and 30% are defective. If three of the products are randomly selected, find the probability that all of them are acceptable.

Find the indicated probability -In one town, 60% of adults have health insurance. What is the probability that 9 adults selected at random from the town all have health insurance?

Provide a written description of the complement of the given event. -When several textbooks are returned from editing, none of the books are found to be errorless.

Provide a written description of the complement of the given event. -When 10 adults are tested for high blood pressure, at least one of the results are positive.

Provide a written description of the complement of the given event. -When 100 engines are shipped, all of them are free of defects.

Find the indicated probability -A bin contains 71 light bulbs of which 9 are defective. If 6 light bulbs are randomly selected from the bin with replacement, find the probability that all the bulbs selected are good ones.