Question 1

A package contains 9 candy canes, 2 of which are cracked. If 2 are selected, find the probability of getting exactly one cracked candy cane.

Accepted Answer

The answer of A package contains 9 candy canes, 2...

Question 2

In a shop there are 45 customers, 14 of whom will make a purchase. If three customers are selected, one at a time, at random, what is the probability that all will make a purchase?

Accepted Answer

The probability that the first customer makes a purchase is 14/45. If the first customer makes a purchase, the probability that the second customer also makes a purchase is 13/44. If the first two customers make a purchase, the probability that the third customer also makes a purchase is 12/43. Multiplying these probabilities gives (14/45) * (13/44) * (12/43) = 0.0257.

Question 3

Find the probability of randomly selecting three science books and four history books from a box containing five science books and six history books.

Accepted Answer

The answer of Find the probability of randomly selecting three...

Question 4

A multiple-choice quiz consists of fifteen questions. Each question has four responses, and only one of the answers is correct. Find the probability of guessing and getting exactly two correct. Round to four decimal places, if necessary.

Accepted Answer

The probability of guessing a correct answer is 0.25, and the probability of guessing incorrectly is 0.75. Using the binomial probability formula P(X=k) = C(n, k) * p^k * (1-p)^(n-k), where n=15, k=2, and p=0.25, the probability is approximately 0.1559.

Question 5

Decide whether the probability described is classical or empirical. Six out of thirty gorillas seen on a safari were female, so the probability of the next gorilla that is seen being female is 0.2.

Accepted Answer

This probability is empirical because it is based on observed data from the safari, not on theoretical reasoning.

Question 6

A box contains five blue, eight green, and three yellow marbles. If a marble is selected at random, what is the probability that it is blue or green?

Accepted Answer

The total number of marbles is 5 (blue) + 8 (green) + 3 (yellow) = 16. The number of favorable outcomes (blue or green) is 5 + 8 = 13. Therefore, the probability is 13/16.

Question 7

The children at a certain school were asked what they prefer to drink with their lunch, and the following table summarizes the children's responses.

$\begin{array}{c|c}
\text { Drink } & \text { Percentage } \
\hline \text { soft drinks } & 48 \
\text { milk/chocolate milk } & 27 \
\text { water } & 15 \
\text { tea } & 5 \
\text { other } & 5
\end{array}$

The school only serves milk, chocolate milk, or water with lunch. What is the probability that the first student in line for lunch will be served their preferred beverage with their lunch?

Accepted Answer

The answer of The children at a certain school were...

Question 8

At a particular college, 32% of the students live in campus housing. If 6 students are in line at the campus bookstore, what is the probability that exactly 2 of them live in campus housing? Round to four decimal places, if necessary.

Accepted Answer

The answer of At a particular college, 32% of the...

Question 9

Three coins are tossed. Find the probability that all the coins land heads up

Accepted Answer

The answer of Three coins are tossed. Find the probability...

Question 10

The odds in favor of an event are 10:1. Find the probability that the event will occur. A) $\frac { 9 } { 10 }$

B) $\frac { 1 } { 10 }$

C) $\frac { 10 } { 11 }$

D) $\frac { 9 } { 11 }$

Accepted Answer

The answer of The odds in favor of an event...

Question 11

A single card is drawn from an ordinary 52-card deck. Find the probability of getting a club or an 8.

Accepted Answer

There are 13 clubs and 4 eights in a deck. However, one of the eights is a club, so we must subtract it to avoid double-counting. Thus, there are 13 + 3 = 16 favorable outcomes. The probability is 16/52 = 4/13.

Question 12

A single card is drawn from an ordinary 52-card deck. Find the probability of getting an 8.

Accepted Answer

There are 4 eights in a 52-card deck (one for each suit: hearts, diamonds, clubs, spades). The probability of drawing an 8 is the number of favorable outcomes (4) divided by the total number of possible outcomes (52), which simplifies to 1/13.

Question 13

When a single card is drawn from a shuffled deck of cards, find the odds against getting a jack.

Accepted Answer

There are 4 jacks in a deck of 52 cards. The odds against drawing a jack are calculated as the number of non-jack cards (48) to the number of jack cards (4), which simplifies to 12:1.

Question 14

Find both the number of combinations and the number of permutations for the given numberof objects. 11 objects taken 7 at a time A) ${ } _ { 11 } C _ { 7 } = 7920$
${ } _ { 11 } P _ { 7 } = 39,916,800$

B) ${ } _ { 11 } C _ { 7 } = 330$
${ } _ { 11 } P _ { 7 } = 1,663,200$

C) ${ } _ { 11 } C _ { 7 } = 39,916,800$
${ } _ { 11 } P _ { 7 } = 7920$

D) ${ } _ { 11 } C _ { 7 } = 1,663,200$
${ } _ { 11 } P _ { 7 } = 330$

Accepted Answer

The answer of Find both the number of combinations and...

Question 15

To win a prize, a person must select 5 numbers from 9 numbers without replacement. Find the probability of winning if a person buys one ticket. (Note: The numbers can be selected in any order.) Round to four decimal places, if necessary.

Accepted Answer

The total number of ways to choose 5 numbers from 9 is given by the combination formula C(9,5) = 126. Since there is only one winning combination, the probability is 1/126, which is approximately 0.0079.

Quiz 11: Statistics