3) In a study, a subject is told that a hand of cards held by the experimenter contain either a star, a circle, a triangle or a square. The experimenter holds five cards in hand, and the subject must guess the shape on each card. The subject has a probability of 0.25 (i.e. %) of guessing correctly on each card. a) If the subject guesses two shapes correctly and three incorrectly, in how many ways can you arrange the sequence of correct and incorrect guesses? b) Assuming that the subject's guesses are independent of one another, calculate the probability that the subject guesses the shape correctly on the first and last card, but incorrectly on the other cards. c) Assuming the subject's guesses are independent of each other, calculate the probability that the subject guesses the shape correctly on exactly two of five cards.

We randomly select a batch of 40 computer disks for shipment. The probability of selecting a good disk is the same as the probability of selecting a defective disk. In part C, you will determine the probability that this shipment contains 10 defective disks and 30 good disks for our batch or 15 defective disks and 25 good disks for our batch. Note: I am not asking for an example of an outcome, although I may ask for examples of outcomes on the exam. A. What is the size of your sample space S? i.e., How many different outcomes (batches of 40 disks) in your sample space? What are the conditions? What counting technique(s) are you using? B. How many outcomes when randomly selecting 10 defective disks and 30 good disks for our batch or 15 defective disks and 25 good disks for our batch. What are the conditions? What counting technique(s) are you using? C What is the probability of randomly selecting a batch of 10 defective disks and 30 good disks or a batch of 15 defective disks and 25…

Two dice, a 8-sided one and a  10-sided one are shaken in a cup then "rolled" onto a table.  How many possible outcomes are there?

A slot machine has 3 dials. Each dial has 30 positions, one of which is "Jackpot". To win the jackpot, all three dials must be in the "Jackpot" position. Assuming each play spins the dials and stops each independently and randomly, what are the odds of one play winning the jackpot?    1/30 = 0.03 or 3%   3/(30+30+30) = 3/90 = 0.33 or 33%   3/(30×30×30) = 3/27000 = 0.0001 or 0.01%   1/(30×30×30) = 1/27000 = 0.00003 or 0.003%     Question 18