$$10 \times 9 \times 8 \times 7 = 5040$$

$$\frac{1}{2} \times \frac{5}{8} = \frac{5}{16}$$

$$\frac{4}{52} \times \frac{4}{51} = \frac{16}{2652}$$

$$P(A) + P(B) - P(A \text{ and } B)$$

Question 1

Which of the following best describes a probability experiment?

Accepted Answer

An action or trial in which specific results (counts, measurements, or responses) are obtained.

Question 2

If you toss a coin and roll a die at the same time, what is the sample space for the outcomes?

Accepted Answer

$$\{H1, H2, H3, H4, H5, H6, T1, T2, T3, T4, T5, T6\}$$

Question 3

A factory produces parts, and you randomly select a part from a batch made today. Is the event of selecting a defective part a simple event?

Accepted Answer

Yes, because it consists of a single outcome.

Question 4

How many possible outcomes are there when determining blood type (O, A, B, AB) and Rh factor (positive or negative)?

Accepted Answer

$$4 	imes 2 = 8$$

Question 5

Using the Fundamental Counting Principle, how many different ways can you choose a car if there are 3 makes, 2 sizes, and 4 colors?

Accepted Answer

$$3 	imes 2 	imes 4 = 24$$

Question 6

If you create a 4-digit PIN and digits cannot be repeated, how many possible PINs are there?

Accepted Answer

$$10 	imes 9 	imes 8 	imes 7 = 5040$$

Question 7

What is the theoretical probability of drawing a heart from a standard deck of 52 cards?

Accepted Answer

$$\frac{13}{52} = \frac{1}{4}$$

Question 8

A survey finds that 765 out of 3000 employees are aged 25-34. What is the empirical probability that the next employee surveyed is in this age group?

Accepted Answer

$$\frac{765}{3000} = 0.255$$

Question 9

If the probability of an event is $$0.05$$, how would you describe the likelihood of this event?

Accepted Answer

Unlikely to occur

Question 10

What is the complement of the event 'an employee is aged 25-34' if $$P(25-34) = 0.255$$?

Accepted Answer

$$1 - 0.255 = 0.745$$

Question 11

If you toss a coin and spin a spinner with 8 equal parts, what is the probability of getting heads and spinning a number greater than 3?

Accepted Answer

$$\frac{1}{2} 	imes \frac{5}{8} = \frac{5}{16}$$

Question 12

What is the probability of selecting a king and then a queen from a deck of 52 cards, without replacement?

Accepted Answer

$$\frac{4}{52} 	imes \frac{4}{51} = \frac{16}{2652}$$

Question 13

Which of the following pairs of events are independent?

Accepted Answer

Tossing a coin and rolling a die

Question 14

If the probability of a surgery being successful is $$0.95$$, what is the probability that all three surgeries are successful?

Accepted Answer

$$(0.95)^3 = 0.857375$

Question 15

Which formula should be used to find the probability of A or B for non-mutually exclusive events?

Accepted Answer

$$P(A) + P(B) - P(A 	ext{ and } B)$$

Question 16

A card is drawn from a standard deck. What is the probability that it is a 4 or an ace?

Accepted Answer

$$\frac{4}{52} + \frac{4}{52} = \frac{8}{52} = \frac{2}{13}$$

Question 17

If the probability of rolling a number less than 3 or an odd number on a die is sought, which formula applies?

Accepted Answer

$$P(	ext{less than 3}) + P(	ext{odd}) - P(	ext{less than 3 and odd})$$

Question 18

In a survey, 560 out of 1502 adults read print books last year. What is the probability that the next adult surveyed read print books?

Accepted Answer

$$\frac{560}{1502} \approx 0.373$$

Probability and Counting Principles in Statistics: Study Notes Chapter. 3

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