# probability

1. ### Probability Question #1

2. The phone lines to an airline reservation system are occupied 40% of the time. Assume that the events that the lines are occupied on successive calls are independent. Assume that 10 calls are placed to the airline. What is the expected number of calls in which the lines are all occupied
2. ### Fair Play Value calculation

A coin is weighted so it comes up head 3/4 of the time and tails 1/4 of the time. You play a game where this coin is flipped. If it comes up heads, you must pay 1 dollar. If it comes up tails, you win 2 dollars. What is the Expected Value of your winnings in this game? I solved this portion...
3. ### Drawing Two Coins

Define a sample space for the experiment of drawing two coins from a purse that contains two quarters, three nickels, one dime, and four pennies. Q - Quarter N - Nickel D - Dime P - Penny S = {QQ, QN, QP, QD, DN, DP, NP, NN, PP} This is the book answer. I am wondering why the sample space did...
4. ### How many times do I need to subsample to sample all?

Lets say I have 10 million unique balls and I plan to subsample 1 million of the balls without replacement multiple times. Each time I go to subsample 1 million new balls, however, the balls will be replaced. How many times do I need to subsample the have subsampled all 10 million of the unique...
5. ### Probability for 15 out of 15 apples to be good when every 10 apple is bad

Sub-questions: Experience shows that 1 in 10 apples is bad. You buy a bag of 15 apples. What is the probability that a) all apples are good, b) all apples are bad? What number of bad apples is most likely to be in the bag? I really think it is easy to solve...I would really appreciate some...
6. ### I am stuck in this probability question and i need some help to find out

Spares of a particular component are produced by two firms , Bestbits and Lesserprod. Tests show that, on average, I in 200 components produced by Bestbits fail within one year Of fitting, and I in 50 components produced by Lesserprod fail within One year Of fitting. Given that 20 per cent of...
7. ### Family of Three Children - Conditional Probability

From families with three children, a family is selected at random and found to have a boy. What is the probability that the boy has (a) an older brother and a younger sister; (b) an older brother; (c) a brother and a sister? Assume that in a three-child family all gender distributions have equal...
8. ### Probability - CDF Given

My answer is 0.9 - 2/4 = 0.4 but the instructor answer is 0.5 + 0.15 = 0.65 I don't understand
9. ### Coin Tossing Problems...

Hi Everyone, New to the forum. Terrible at math. I'm enrolled in a college Math 100 course, and I'm having some trouble understanding some concepts related to combinations, permutations, Pascal's Triangle, etc. Here are the problems I'm stuck on: Suppose 9 fair coins are tossed. Find the...
10. ### Cards probability

I draw 9 cards out of a deck of 52 cards. what's the probability that i draw one of them 4 times (different shape). no returns to the deck. thanks!
11. ### I need help in understanding and solving this question

When an assembly machine is properly calibrated approximately 5% of the finished products are defective. Periodically the quality control engineer randomly selects 20 products at random and tests them. He will halt the production line to check (and reconfigure, if necessary) the calibration if...
12. ### demonstration with discrete random variable

I would like to know if anybody from this forum have some insights about how to handle this demonstration: "Show that for any discrete random variable X, etE[X] <= E[etX], where t is fixed and belongs to R." (E is expected value) Maybe this is related with Jansen inequality, but certainly I'm...
13. ### Request about a problem with a die

Dear members. I recently started a statistics course, but I'm having a hard time with some problems like the one I'm requesting help from you. Suppose a fair die with faces 1 to 6 is rolled 20 times. Now we define the random variable: the maximum value observed from the 20 rolls. What is the...
14. ### Probability based question

Consider two independent events, A and B, where the P(A) is 0.45 and the probability that A does not occur or B occurs is 0.70. Determine the probability that event B occurs. Any help is greatly appreciated :)
15. ### Inverse Z-Transform vs inverse PGF?

The "official" formula for obtaining the inverse Z-Transform is $$x[n] = \frac{1}{2\pi i}\oint_\Gamma z^{n-1} X(z) dz,$$ where $\Gamma$ is any counterclockwise closed path containing the origin and entirely in the ROC. Compare this formula to the formula that allows to extract a probability...
16. ### Calculating lottery probabilities

The lottery i am talking about is a 6/49 game. You select 6 numbers from a pool of 49, and in the draw 6 numbers are taken. There is also an additional 'Bonus' number drawn from the remaining 43 balls which is used in some of the prize tiers. I have managed to calculate the overall odds of...
17. ### Trees probability, p-value

for question d and e? The mean difference between the two groups (fertilizer and control) is the -0.965. so thus we can consider 2 explanations for the -0.965 difference The fertilizer has no effect on the height of popular trees and diff. of -0.965 was due to chance. The diff. of...
18. ### Tricky question (tree diagram)

A randomised response technique was used to investigate rates of illegal fishing of red abalone in Northern California. The study involved interviews with people at various sites. Once verbal consent to participant was obtained, each respondent was given a coin and an envelope containing two...

20. ### What is the standard deviation of the measurements coverted into Celsius?

A temperature measurment F in degrees Fahrenheit can be converted to a measurement C in degrees Celsius using the formula C=(5/9) (F-32). Suppose 10 measurments in Fahreheit have a mean of 86 degrees and a standard debiation of 3.4 degrees. What is the standard deviation of the measurements...