Question

Assignment 2

1. Assume that you have two biased coins and one fair coin. One of the biased coins are two tailed and the second biased one comes tails 25 percent of the time. A coin is selected randomly and flipped. What is the probability that the flipped coin will come up tail?

2. One white ball, one black ball, and two yellow balls are placed in a bucket. Two balls are drawn simultaneously from the bucket. You are given the information that at least one of them is yellow. What is the probability that the second ball is also yellow?

3. Students taking the GMAT were asked about their undergraduate major and intent to pursue their MBA as a full-time or part-time student. A summary of their responses follows. a. If a student intends to attend classes full-time in pursuit of an MBA degree, what is the probability that the student was an undergraduate engineering major? b. If a student was an undergraduate business major, what is the probability that the student intends to attend classes full-time in pursuit of an MBA degree?

4. Two fair dice are rolled and the upper sides (faces) are recorded. Given information that the sum of the faces equals to 10, what is the probability that the first one has a 5 on the face?

5. You roll a 12-sided die with equal probability of having the numbers 1 through 12 on the upper side. Your friend covers up the number it shows, but you are given the information that it only has one digit (and therefore can't be 10, 11 and 12). What is the probability it has 5 on the upper side?

6. The crosstabulation below represents the number of households (1,000s) and the household income by the highest level of education for the head of the household. Use the crosstabulation to answer the following questions. a. What is the probability a household is headed by someone with a high school diploma earning $100,000 or more? b. What is the probability a household is headed by someone with a bachelor’s degree earning less than $25,000?

7. 100 high school students are asked if they speak German. 70% of male students answer that they do not speak German, while 40% of female students answer they speak German. It is known that 40% of the responding students are female. If a randomly chosen student answers that he/she speaks German, what is the probability that this student is a female?

8. In a hospital, 30% of the staff are female, and 50% of the staff walk to hospital. If 20% of the staff is female and walk to hospital, what is the probability that a randomly chosen staff is female or walks to hospital?

9. A card is drawn randomly from a standard deck of cards. What is the probability that the card drawn is a 2 or a Spade? Details and Assumptions: A standard deck of cards consists of 52 cards, formed by 13 ranks (Ace, 2, 3, 4, 5, 6, 7, 8, 9, 10, Jack, Queen and King) of 4 suits (clubs, diamonds, hearts and spades).

Answer 1

We would be looking at the first question here.

As each of the 3 coins is randomly selected, therefore, we have here:
P(coin 1) = P(coin 2) = P(coin 3) = 1/3

Also for the three coins, we are given here that:
P( tail | coin 1) = 0.5
P( tail | coin 2) = 1
P( tail | coin 3) = 0.25

Therefore using law of total probability, we get here:
P( tail ) = P(tail | coin 1)P(coin 1) + P(tail | coin 2)P(coin 2) + P(tail | coin 3)P(coin 3)

P(tail) = (1/3)*(0.5 + 1 + 0.25) = 0.5833

Therefore 0.5833 is the required probability of getting a tail here.