Someone has stolen an ATM card and knows that the first and last digits of the PIN are 5 and 1, respectively. He has three tries before the card is retained by the ATM (but does not realize that). So he randomly selects the 2nd and 3rd digits for the first try, then randomly selects a different pair of digits for the second try, and yet another randomly selected pair of digits for the third try (the individual knows about the restrictions described in (b) so selects only from the legitimate possibilities). What is the probability that the individual gains access to the account?

In a classic study of problem solving, Duncker (1945) asked participants to mount a candle on a wall in an upright position so that it would burn normally. One group was given a candle, a book of matches, and a box of tacks. A second group was given the same items, except that the tacks and the box were presented separately as two distinct items. The solution to this problem involves using the tacks to mount the box on the wall, creating a shelf for the candle. Duncker reasoned that the first group of participants would have trouble seeing a new function for the box (a shelf) because it was already serving a function (holding tacks). For each participant, the amount of time to solve the problem was recorded. Data similar to Duncker’s are as follows.             Time to Solve Problem (in sec.)                     Box of Tacks                       Tacks and Box Separate         128                                                42         160…

Emma's v he-Go, a large convenience store that makes a good deal of money from magazine sales, has three possible locations in the store for its magazine rack: in uie iront of the store (to attract "impulse buying" by all customers), on the left-hand side of the store (to attract teenagers who are on that side of the store looking at the candy and soda), and in the back of the store (to attract the adults searching through the alcohol cases). The manager at Emma's experiments over the course of several months by rotating the magazine rack among the three locations, choosing a sample of 42 days at each location. Each day, the manager records the amount of money brought in from the sale of magazines. Below are the sample mean daily sales (in dollars) for each of the locations, as well as the sample variances: Sample Sample Sample size Group mean variance Front 42 225.4 453.5 Left-hand side 42 223.9 506.8 Right-hand side 42 211.6 393.6 Send data to calculator Send data to Excel Suppose…

A box has 10 red balls, 10 green balls, 10 blue balls and 10 yellow balls, and for each colour the balls are labelled1,2, ..., 10. Suppose five balls are chosen from the box. (a) How many ways can you choose 5 balls (with no further constraints)? (b) How many ways can you choose 5 balls so that exactly 4 of them are the same colour? (c) How many ways can there be three of one colour and two of another colour.