Q: Suppose you toss a coin 200 times and observe 110 heads. Using the empirical probability formula, what is the probability of getting a head?

$$P(\text{head}) = \frac{110}{200} = 0.55$$

Q: If you draw a single card from a standard deck, what is the probability that it is a heart?

$$P(\text{heart}) = \frac{13}{52} = 0.25$$

Q: If the probability that a randomly selected 60-year-old female survives the year is 0.99186, what is the probability that two randomly selected 60-year-old females both survive the year?

$$P = 0.99186 \times 0.99186 = 0.9838$$

Q: Which formula correctly expresses the conditional probability of event F given event E?

$$P(F|E) = \frac{P(E \text{ and } F)}{P(E)}$$

Q: Which rule should you use to find the probability of drawing a red card or a queen from a standard deck of cards?

$$P(E \text{ or } F) = P(E) + P(F) - P(E \text{ and } F)$$

Question 1

Which of the following best describes the Law of Large Numbers as illustrated by the coin flip graphs in the first image?

Accepted Answer

As the number of coin flips increases, the proportion of heads will get closer to the theoretical probability of 0.5.

Question 2

Suppose you toss a coin 200 times and observe 110 heads. Using the empirical probability formula, what is the probability of getting a head?

Accepted Answer

$$P(	ext{head}) = \frac{110}{200} = 0.55$$

Question 3

In the Venn diagram shown, what does the region labeled '13' represent?

Accepted Answer

The outcomes that are in both events E and F.

Question 4

If you draw a single card from a standard deck, what is the probability that it is a heart?

Accepted Answer

$$P(	ext{heart}) = \frac{13}{52} = 0.25$$

Question 5

Which formula would you use to find the probability that a randomly selected household does NOT own a dog, given that 31.6% of households own a dog?

Accepted Answer

$$P(E^c) = 1 - P(E)$$

Question 6

If the probability that a randomly selected 60-year-old female survives the year is 0.99186, what is the probability that two randomly selected 60-year-old females both survive the year?

Accepted Answer

$$P = 0.99186 	imes 0.99186 = 0.9838$$

Question 7

Which formula correctly expresses the conditional probability of event F given event E?

Accepted Answer

$$P(F|E) = \frac{P(E 	ext{ and } F)}{P(E)}$$

Question 8

A committee of 3 people is to be chosen from 8 candidates. How many different committees are possible?

Accepted Answer

$$\binom{8}{3} = 56$$

Question 9

How many different ways can the letters M, A, T, H be arranged if all letters must be used and no letter is repeated?

Accepted Answer

$$4! = 24$$

Question 10

A bag contains 5 white, 3 blue, and 2 red flags. How many different vertical arrangements are there of all 10 flags?

Accepted Answer

$$\frac{10!}{5!3!2!}$$

Question 11

Which of the following scenarios best illustrates the use of subjective probability?

Accepted Answer

An economist predicts a 20% chance of recession next year based on their judgment.

Question 12

If you are forming a password using 7 lowercase letters and repetition is allowed, how many different passwords are possible?

Accepted Answer

$$26^7$$

Question 13

Which rule should you use to find the probability of drawing a red card or a queen from a standard deck of cards?

Accepted Answer

$$P(E 	ext{ or } F) = P(E) + P(F) - P(E 	ext{ and } F)$$

Question 14

A track event has 8 athletes and 3 medals (gold, silver, bronze) to award. How many different orderings of the top three athletes are possible?

Accepted Answer

$$P(8,3) = \frac{8!}{(8-3)!} = 336$$

Question 15

If the probability that a randomly selected item is defective is 0.02, what is the probability that at least one item is defective in a sample of 10, assuming independence?

Accepted Answer

$$1 - (1 - 0.02$$)^{10}$$

Question 16

Which counting technique should you use if you are selecting 3 books from a shelf of 10, and the order in which you select them does NOT matter?

Accepted Answer

Combinations: $$\binom{10}{3}$$

Question 17

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

Accepted Answer

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

Chapter 5: Probability – Comprehensive Study Notes

Guida di studio - Domande di pratica

Study guide - Flashcard