Q: If two events E and F are independent, which of the following is TRUE?

$$ P(E \cap F) = P(E) \times P(F) $$

Q: A bag contains 5 red, 4 blue, and 3 green marbles. If two marbles are drawn at random without replacement, what is the probability that both are red?

$$ \frac{5}{12} \times \frac{4}{11} $$

Question 1

Which of the following statements about probability models is TRUE?

Accepted Answer

The sum of the probabilities of all possible outcomes must equal 1.

Question 2

Suppose a bag contains 20 red balls, 30 blue balls, and 50 green balls. If one ball is drawn at random, what is the probability that it is blue?

Accepted Answer

$$ \frac{3}{10} $$

Question 3

A probability is interpreted as:

Accepted Answer

A measure of the likelihood of a random phenomenon or chance behavior.

Question 4

A fair coin is flipped 10 times. What is the probability of getting exactly 7 heads? (Use the binomial formula: $$ P(X = k) = \binom{n}{k} p^k (1-p$$)^{n-k}$$ $$ with $$ p = 0.5 )$$

Accepted Answer

$$ \binom{10}{7} (0.5$$)^{10}$$ $$

Question 5

In a probability model, which of the following numbers could NOT be the probability of an event?

Accepted Answer

$$ 1.2 $$

Question 6

A survey of 800 randomly selected high school students found that 320 play organized sports. What is the probability that a randomly selected student plays organized sports?

Accepted Answer

$$ \frac{320}{800} $$

Question 7

A standard deck of 52 cards contains 13 hearts. What is the probability of randomly selecting a heart?

Accepted Answer

$$ \frac{1}{4} $$

Question 8

If $$ P(A) = 0.3 $$ and $$ P(B) = 0.5 $$, and A and B are mutually exclusive, what is $$ P(A \cup B) $$?

Accepted Answer

$$ 0.8 $$

Question 9

A probability experiment consists of rolling two six-sided dice. What is the probability that the sum is 7?

Accepted Answer

$$ \frac{6}{36} $$

Question 10

Which of the following best describes an unusual event?

Accepted Answer

An event with a probability close to 0.

Question 11

Suppose the probability that a randomly selected person has a birthday in July is $$ \frac{31}{365} . $$What is the probability that a randomly selected person does NOT have a birthday in July?

Accepted Answer

$$ 1 - \frac{31}{365} $$

Question 12

If two events E and F are independent, which of the following is TRUE?

Accepted Answer

$$ P(E \cap F) = P(E) 	imes P(F) $$

Question 13

A bag contains 5 red, 4 blue, and 3 green marbles. If two marbles are drawn at random without replacement, what is the probability that both are red?

Accepted Answer

$$ \frac{5}{12} 	imes \frac{4}{11} $$

Question 14

A probability experiment is conducted in which the sample space is $$ S = \{1, 2, 3, 4, 5, 6\} . $$Let event $$ E = \{2, 4, 6\} . $$What is $$ P(E)  if $$each outcome is equally likely?

Accepted Answer

$$ \frac{3}{6} $$

Question 15

A company wants to send two employees to a statistics conference. If there are 5 employees, how many different pairs can be selected?

Accepted Answer

$$ \binom{5}{2} $$

Question 16

If $$ P(A) = 0.4 $$, $$ P(B) = 0.5 $$, and $$ P(A \cap B) = 0.2 $$, what is $$ P(A \cup B) $$?

Accepted Answer

$$ 0.7 $$

Question 17

A probability model assigns probabilities to outcomes such that:

Accepted Answer

Each probability is between 0 and 1, and the sum of all probabilities is 1.

Question 18

A bag contains 10 bulbs: 4 red, 4 yellow, and 2 purple. If a bulb is selected at random, what is the probability that it is not purple?

Accepted Answer

$$ \frac{8}{10} $$

Question 19

If $$ P(E) = 0.3 $$ and $$ P(F) = 0.4 $$, and E and F are disjoint, what is $$ P(E \cup F) $$?

Accepted Answer

$$ 0.7 $$

Question 20

A probability experiment consists of spinning a wheel with 8 equal sectors numbered 1 to 8. What is the probability that the spinner lands on an even number?

Accepted Answer

$$ \frac{4}{8} $$

Probability Models and Basic Probability Concepts: Study Notes

Guida di studio - Domande di pratica

Study guide - Flashcard