CS 2203 Statistics and Probability Lec 3: Dependent Events

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What are the odds that it will rain on Saturday, given a 75% chance of rain?

3/1

What does the 75% chance of rain on Saturday mean?

The probability of it raining on Saturday is 75%.

In a situation where it rained on 75 out of 100 days with similar conditions to Saturday, what are the odds of rain?

3/1

What are the odds of drawing an ace at random from a standard deck of cards?

4/48 Signup and view all the answers

Define independent events and provide an example.

Independent events are events where the outcome of one event does not affect the outcome of another event. An example is selecting a marble from a container and selecting an ace from a deck of cards. Signup and view all the answers

Define dependent events and provide an example.

Dependent events are events where the outcome of one event affects the outcome of another event. An example is drawing two cards from a deck without replacement. Signup and view all the answers

If you roll two fair dice, what is the total number of possible outcomes in the sample space?

36 Signup and view all the answers

Construct a table to represent the sample space of rolling a single fair die and tossing a fair coin.

| Die | Coin ||-----|------|| 1 | Heads|| 1 | Tails|| 2 | Heads|| 2 | Tails|| 3 | Heads|| 3 | Tails|| 4 | Heads|| 4 | Tails|| 5 | Heads|| 5 | Tails|| 6 | Heads|| 6 | Tails| Signup and view all the answers

If you randomly select a card from a standard deck of 52 cards, what is the probability of selecting a heart?

$\frac{13}{52}$ or $\frac{1}{4}$ Signup and view all the answers

Give an example of a random experiment with dependent events.

Choosing a jack from a deck of cards, then choosing another jack without replacing the first card. Signup and view all the answers

In how many ways can you select a sandwich and a side from a menu with 5 sandwich options and 3 side options?

15 Signup and view all the answers

Provide an example of a random experiment with independent events.

Rolling a number less than 4 on one die and rolling an even number on a second die. Signup and view all the answers

In a bag containing 5 red balls and 3 green balls, what is the probability of drawing a red ball and then a green ball without replacement?

$P(\text{red, green}) = \frac{5}{8} \times \frac{3}{7}$ Signup and view all the answers

A box contains 4 white balls and 2 black balls. If two balls are drawn at random without replacement, how many outcomes are in the sample space?

15 Signup and view all the answers

Construct a probability distribution table for rolling two fair dice, listing all possible outcomes and their respective probabilities.

See table below: <table> <thead> <tr> <th>Sum</th> <th>Outcomes</th> <th>Probability</th> </tr> </thead> <tbody> <tr> <td>2</td> <td>(1,1)</td> <td>1/36</td> </tr> <tr> <td>3</td> <td>(1,2), (2,1)</td> <td>2/36</td> </tr> <tr> <td>...</td> <td>...</td> <td>...</td> </tr> <tr> <td>12</td> <td>(6,6)</td> <td>1/36</td> </tr> </tbody> </table> Signup and view all the answers

If a coin is tossed twice, what is the probability of getting at least one head?

$\frac{3}{4}$ Signup and view all the answers

A bag contains 3 red balls and 2 blue balls. If a ball is drawn at random, found to be red, and then returned to the bag, what is the probability that the second draw is also red?

$\frac{3}{5}$ Signup and view all the answers

In a statistics class of 25 students, 15 are economics majors. If 3 students are selected at random without replacement, what is the probability that 2 are economics majors?

$\frac{15}{25} \times \frac{14}{24} \times \frac{10}{23}$ Signup and view all the answers