Independent and Dependent Events Worksheet Answers

Honors Algebra 2 10.2 - Independent and Dependent Events Name: Trollope Date: 1. Explain the difference between independent and dependent events, and give an example of each. **When events   are independent, the occurrence of one event does NOT affect the other. When events are dependent, the occurrence of one event affects the other.** **Example of Independent Events:** - Rolling a die and flipping a coin. - The outcome of one event doesn't affect the other. **Example of Dependent Events:** - Drawing two cards from a deck without replacement. - The outcome of the first draw affects the probability of the second draw. In Exercises 2 and 3, tell whether the events are independent or dependent. Explain your reasoning. 2. You and a friend are picking teams for a softball game. You randomly choose a player. Then your friend randomly chooses   a player. Event A: You choose a pitcher. Event B: Your friend chooses a first baseman.   **Dependent, because a player cannot be chosen for both teams.** 3. You are making bracelets for party favors. You randomly choose a charm and a piece of leather. Event A: You choose a heart-shaped charm first. Event B: You choose a brown piece of leather second.   **Independent, the picking of a charm does not affect the choices of leather.** 4. A sack contains the 26 letters of the alphabet, each printed on a separate wooden tile. You randomly draw one letter, and then you randomly draw a second letter. Find the probability of each pair of events.   a. You replace the first letter before drawing the second letter. Event A: The first letter drawn is T.   P(A) = 1/26 Event B: The second letter drawn is A. P(B) = 1/26 P(A and B) = 1/26 * 1/26 = 1/676 = 0.0015 = 0.15% b. You do not replace the first letter tile before drawing the second letter tile. Event A: The first letter drawn is P. P(A) = 1/26 Event B: The second letter drawn is S. P(B) = 1/25 P(A and B) = 1/26 * 1/25 = 1/650 = 0.0015 = 0.15% 5. You play a game that involves drawing two numbers from a hat. There are 25 pieces of paper numbered from 1 to 25 in the hat. Each number is replaced after it is drawn. Find the probability that you will draw   the number 1 on your first draw and a number greater than 10 on your second draw.   P(1 and >10) = P(1) * P(>10) = 1/25 * 15/25 = 0.024 = 2.4% 6. Events A and B are independent. Suppose P(B) = 0.4 and P(A and B) = 0.13. Find P(A). P(A and B) = P(A) * P(B) 0.13 = P(A) * 0.4 P(A) = 0.325 7. Events A and B are dependent. Suppose P(B|A) = 0.6 and P(A and B) = 0.15. Find P(A). P(A and B) = P(A) * P(B|A) 0.15 = P(A) * 0.6 P(A) = 0.25 8. A word game has 100 tiles, 98 of which are letters and 2 of which are blank. The number of tiles of each letter are shown. You randomly draw I tile, set it aside, and then randomly draw another tile. Find the probability that both events A and B will occur. Event 4: The first tile is a consonant. Event B: The second tile is a vowel. 56/100 * 42/99 = 2352/9900 ]= 196 825 = 0.238 * 23.8 \% 42 56 cons. -9-2-8-2 Vowels-2-1-1-1 -4-1-6-2 -12-4-4-1 -3-6-4 Blank 9. You randomly select three cards from a standard deck of 52 playing cards. What is the probability that all three cards are face cards when (a) you replace each card before selecting the next card, and (b) you do not replace each card before selecting the next card? Compare the probabilities. (a) * 12/52 * 12/52 * 12/52 3/13 * 3/13 * 3/13 = boxed 27 2197 =0.012\\ underline 1.2\% (b) 12/52 * 11/51 * 10/50 3/13 * 11/51 * 1/5 = boxed 11 1105 =.001=1.0\% 10. At a high school football game, 80% of the spectators buy a 20% of the spectators buy both a beverage and a food item. What is the probability that a spectator who buys a beverage also buys a food item? P(B/A) = P(A und B) P(A) ===25% 11. The probability that a stock increases in value on a Monday is 60%. When the stock increases in value on Monday, the probability that the stock increases in value on Tuesday is 80%. What is the probability that the stock increases in value on both Monday and Tuesday of a given week? P(Aan * dB) = P(A) P(BIA) 6.8.48487, = 12. When two six-sided dice are rolled, there are 36 possible outcomes. Find the probability that (a) the sum is not 4 and (b) the sum is greater than (a) * 33/36 = boxed 11 12 =0.917 (b) * 26/36 = boxed 13 18 =0.722 13. The scores for a math course test are normally distributed with a mean of 61 and a standard deviation of 11. The test scores range from 0 to 100. a. About what percent of taking the test have scores between 72 and 837 2.35 13.5% 28 39 13.3 5 34 13.5 61 72 8 97 b. About what percent of the students taking the test have scores less than 507 116%