CS 2203 Statistics and Probability Lec 3: Dependent Events

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Questions and Answers

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?

<p>4/48</p>
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Define independent events and provide an example.

<p>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.</p>
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Define dependent events and provide an example.

<p>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.</p>
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If you roll two fair dice, what is the total number of possible outcomes in the sample space?

<p>36</p>
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Construct a table to represent the sample space of rolling a single fair die and tossing a fair coin.

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

<p>$\frac{13}{52}$ or $\frac{1}{4}$</p>
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Give an example of a random experiment with dependent events.

<p>Choosing a jack from a deck of cards, then choosing another jack without replacing the first card.</p>
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In how many ways can you select a sandwich and a side from a menu with 5 sandwich options and 3 side options?

<p>15</p>
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Provide an example of a random experiment with independent events.

<p>Rolling a number less than 4 on one die and rolling an even number on a second die.</p>
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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>$P(\text{red, green}) = \frac{5}{8} \times \frac{3}{7}$</p>
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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?

<p>15</p>
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Construct a probability distribution table for rolling two fair dice, listing all possible outcomes and their respective probabilities.

<p>See table below:</p> <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>
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If a coin is tossed twice, what is the probability of getting at least one head?

<p>$\frac{3}{4}$</p>
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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?

<p>$\frac{3}{5}$</p>
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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?

<p>$\frac{15}{25} \times \frac{14}{24} \times \frac{10}{23}$</p>
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