a. a straight (5 cards of distinct ranks differing by 1),
b. full house flush (2 cards of one suit, 3 of another),
c. two pair.
a. What is the probability that your first choice of two keys is correct?
b. What is the probability that you also put the keys into the correct locks on the first try?
c. Suppose you lose one key. What is the probability that you can still
get in your house (ignore the open window)? Given the lost key,
answer questions a. and b.
a. Compute the probability of this occurrence, assuming the 100 trout are caught all together.
b. Compute the probability of this occurrence, assuming that after each trout is caught it is returned to the lake.
c. Evaluate your expressions for n = 500; 1000; 10,000; 100,000 and compare.
Given that 7 out of 100 are tagged what is your best guess as to the
number of trout n ?
a. We can make an even coarser measurement of the throw of the dice by only accounting for the "coincidence patterns," as in cards: for example, a pair, two pairs, a triple, ... , a sextuple. Enumerate the 11 possible coincidence patterns.
b. There are several ways for each coincidence pattern to be realized: for example, a pair might be two 1's, 3,4,5,6. or two 1's, 2,3,5,6 (order is not important). For each coincidence pattern count the number of ways in which it can occur. The sum over all coincidence patterns should be 462.
c. Taking account now of the color, each realization of a coincidence
pattern can occur in several ways. But this is dependent only on the
coincidence pattern and not on the realization. For each coincidence
pattern find this number. Then add up the appropriate things to get 46,656.
|number||one, two, three|
|shape||oval, peanut, diamond|
|color||red, green, purple|
|shading||solid, striped, empty|
a. How many cards are there?
b. How many distinct sets are there? What is the probability that an arbitrary choice of three cards is a set?