Q: If you draw two cards from a deck without replacement, what is the probability that both are Kings?

$$ \frac{4}{52} \times \frac{3}{51} $$

Q: Sixteen batteries are tested; four fail. If two are selected at random without replacement, what is the probability both fail?

$$ \frac{4}{16} \times \frac{3}{15} $$

Q: A patient has a $$ \frac{6}{10} $$ chance of surviving surgery and a $$ \frac{7}{10} $$ chance of full recovery if they survive. What is the probability the patient survives and makes a full recovery?

$$ \frac{6}{10} \times \frac{7}{10} $$

Q: Which formula represents the multiplication rule for two dependent events A and B?

$$ P(A \text{ and } B) = P(A) \times P(B | A) $$

Q: Given a table of students, if P(algebra) = 0.332 and P(algebra | nursing) = 0.115, are the events 'taking algebra' and 'being a nursing major' independent?

No, because $$ P(algebra) \neq P(algebra | nursing) $$

Q: A patient has a $$ \frac{6}{10} $$ chance of surviving surgery and a $$ \frac{3}{10} $$ chance of not making a full recovery if they survive. What is the probability the patient survives and does not make a full recovery?

$$ \frac{6}{10} \times \frac{3}{10} $$

Question 1

Which of the following best describes conditional probability?

Accepted Answer

The probability of an event occurring, given that another event has already occurred.

Question 2

A deck of 52 cards is used. What is the probability of drawing a Jack and then a Ten, without replacement?

Accepted Answer

$$ \frac{16}{2652} $$

Question 3

Which statement correctly identifies independent events?

Accepted Answer

The probability of the second event is not affected by the occurrence of the first event.

Question 4

You toss a coin three times and get heads each time. What is the probability that the next toss will also be heads?

Accepted Answer

$$ \frac{1}{2} $$

Question 5

If you draw two cards from a deck without replacement, what is the probability that both are Kings?

Accepted Answer

$$ \frac{4}{52} 	imes \frac{3}{51} $$

Question 6

A 5-question multiple choice quiz has 4 possible answers per question. If you guess randomly, what is the probability that all questions are correct?

Accepted Answer

$$ \left( \frac{1}{4} \$$right)^5$$ $$

Question 7

Sixteen batteries are tested; four fail. If two are selected at random without replacement, what is the probability both fail?

Accepted Answer

$$ \frac{4}{16} 	imes \frac{3}{15} $$

Question 8

Given the following data: 1198 students take college algebra out of 3605 total students. What is the empirical probability that a randomly selected student is taking college algebra?

Accepted Answer

$$ \frac{1198}{3605} $$

Question 9

If 57.8% of college-seeking seniors took a standardized test and 64.4% of those plan to submit their score, what is the probability a randomly selected senior took the test and will submit their score?

Accepted Answer

$$ 0.578 	imes 0.644 $$

Question 10

A patient has a $$ \frac{6}{10} $$ chance of surviving surgery and a $$ \frac{7}{10} $$ chance of full recovery if they survive. What is the probability the patient survives and makes a full recovery?

Accepted Answer

$$ \frac{6}{10} 	imes \frac{7}{10} $$

Question 11

What is the probability that at least one battery fails the test when two are selected from sixteen (four failed), without replacement?

Accepted Answer

$$ 1 - \frac{132}{240} $$

Question 12

If the probability of getting a question wrong on a 5-question multiple choice quiz is $$ \frac{3}{4} $$, what is the probability of getting all questions wrong?

Accepted Answer

$$ \left( \frac{3}{4} \$$right)^5$$ $$

Question 13

Which formula represents the multiplication rule for two dependent events A and B?

Accepted Answer

$$ P(A 	ext{ and } B) = P(A) 	imes P(B | A) $$

Question 14

If two events A and B are independent, which of the following is true?

Accepted Answer

$$ P(B | A) = P(B) $$

Question 15

Given a table of students, if P(algebra) = 0.332 and P(algebra | nursing) = 0.115, are the events 'taking algebra' and 'being a nursing major' independent?

Accepted Answer

No, because $$ P(algebra) 
eq P(algebra | nursing) $$

Question 16

A patient has a $$ \frac{6}{10} $$ chance of surviving surgery and a $$ \frac{3}{10} $$ chance of not making a full recovery if they survive. What is the probability the patient survives and does not make a full recovery?

Accepted Answer

$$ \frac{6}{10} 	imes \frac{3}{10} $$

Question 17

If the probability of getting at least one question correct on a 5-question multiple choice quiz is the complement of getting none correct, which formula expresses this probability?

Accepted Answer

$$ 1 - \left( \frac{3}{4} \$$right)^5$$ $$

Question 18

If you draw two cards from a deck with replacement, what is the probability both are Kings?

Accepted Answer

$$ \frac{4}{52} 	imes \frac{4}{52} $$

Question 19

In a survey, 57.8% of seniors took a standardized test. What is the probability that a randomly selected senior took the test and will NOT submit their score, if 64.4% plan to submit?

Accepted Answer

$$ 0.578 	imes (1 - 0.644) $$

Conditional Probability and the Multiplication Rule - 3.2

Guida di studio - Domande di pratica

Study guide - Flashcard