Question
NYCCT MAT2572 Halleck Fall 2017 exam 1 v Consi der an e withdraw di awing a second ball. Draw a tree diagram. Be sure to include labels and probabilities. Use the agram to make a table with outcomes and probabilities. Express all probabilities as fractions lowest terms. There are 2 red, 1 blue and 2 green balls in the box. What is the sample space of this experiment? b. As a set, what is the event A: the two balls drawn are the same color? What is its probability c. a. As a set, what is the event B: the second ball is not green? What is its probability? d. As a set, what is the event A and B? In words, what is the event? Find P(A n B) Use the results from parts b, c & d, to determine whether A and B are independent? If not, does e. one positively or negatively affect the chance of the other? A newspaper has 31.1% of its reporters overseas 17% of those are younger than 30, while only 10.5% of its domestic staff are younger than 30. the situation. Round all answers to the nearest 10h of a% 2. Make a probability tree or a partial one to help you analyze What is the chance that a randomly picked employee works within the USA? b. What is the chance that a randomly picked employee is overseas and is younger than 30? c. What is the chance that a randomly picked employee is overseas or is younger than 30? d. Given that an employee is younger than 30, what is the chance that he or she is overseas? a. Sample space is 3 letter words with just the standard 26 letter English alphabet. Vowels are a, e, i, o and u. Other 21 letters are consonants. 3. a. Let A be the event that word begins with a vowel and has no repeats. Find P(A) b. Let B be the event that the word ends with a consonant and has no repeats. Find P(B) c. Find P(AnB). d. Are A and B independent? If not, does one positively or negatively affect chance of the other? 4. Six cards are pulled from a deck of 52 cards. Find an expression for the probability of obtaining a. At least two hearts b. 3 of a kind c. 3 pair d. Two 3 of a kind A bucket of water contains 5 red apples and x yellow ones. Ron bobs and gets 3 of them (without replacement) 5. a. Find an expression that represents the probability that the It apple b. Find an expression that represents the probability that 2 apples are red and the 3d is yellow, regardless of the order in which they come out. (Bonus 2 pts: use hypergeometric formula to get an expression). If the chance of getting the event described in a. is 1/6, find an equation and use guess and check to determine x (hint, answer is a small positive integer). c. Bonus questions (5 pts each): A. What is a probability function? Be sure to discuss the domain and codomain (range) B. You and your neighbor receive 2 cards from a standard deck. What is the chance that you get 2 cards of consecutive denominations, e.g. ace, 2 or 10, jack)? If you get a straight, how form a straight (a sequence does that affect the chance that your neighbor also gets a straight? Explain.
Explanation / Answer
(According to Chegg policy only one question with four subquestions will be answered. Please post the remaining in another question)
3. a. The number of choices for the first letter are 5 (a,e,i,o,u).
The number of choices for the second letter are 25 (no repeats).
The number of choices for the third letter are 24 (no repeats).
=> Total number of choices with the given pattern = 5*25*24 = 3000.
Total number of three letters = 26 * 26 * 26 = 17576.
Probability P(A) = 3000 / 15756 = 0.1904.
b. The number of choices for the third letter = 21.
The number of choices for the first letter = 25.
The number of choices for the second letter = 24.
=> Total number of choices = 21 * 25 * 24 = 12600.
Probability = 12600 / 15756 = 0.7997
c. P(A B) is the probability that the word begins with a vowel, ends with a consonant and has no repeats.
The first letter has 5 choices.
The second letter has 21 choices.
The third letter has 24 choices.
=> Total number of choices = 5*21*24 = 2520.
Probability = 2520 / 15756 = 0.1599
d. P(A) P(B) = 0.1904 * 0.7997 = 0.1523
Since P(A) P(B) has a value different from P(A B), the events are not independent. If A takes place, the probability of B taking place decreases and vice versa. So they negatively affect each others' chances.
