Q1. In the Poker game, a hand is a set of 5 cards chosen randomly from a usual deck of 52 cards.
a) How many straight flush possible hands exist in Poker? (5 cards of 5 consecutive ranks, all in 1 suit, including Aces, Kings, Queens and Jacks). Explain.
b) How many full house possible hands exist in Poker? (3 cards of the same rank and 2 of another rank, for example, 3 Aces and 2 Jacks). Explain.
c) What is the probability of one hand of Poker be a flush? (5 cards of 1 suit, for example, 2, 5, Ace, Jack and 10 of hearts). Explain.
d) What is the probability of one hand of Poker be a two pair? (2 cards in each of 2 different ranks, and a 5th card of a third rank, for example, two Aces, two Jacks and one 10). Explain.
Q2. Let ? be a space of results and B one happening such that probability of B > 0 (P(B) > 0). Prove that for any happening A, we have:
P(A|B) + P(?\ A|B) = 1
Q3. In a Phone Central, we observe, every minute, if certain phone line is or is not occupied. In this way, it has been told that the probability of certain line is occupied in certain moment, if in the last minute was free, is 30% and the probability of certain line is free if in the last minute was occupied is 25%.
a) Identify the space of results of an observation of 2 consecutive minutes.
b) Identify the probability of certain line be free if in the last minute was free.
c) If certain line is occupied in a certain moment, what is the probability of that line be free in the next minute? Explain.
Q4. In the next table we present data relative to the annual production of acorn ant the mean weight of pigs created in certain farm property, in the last six years.
Table:
|
Acorn produced (ton)
|
10
|
17
|
32
|
35
|
38
|
48
|
|
Mean weight (kg)
|
95
|
107
|
101
|
97
|
98
|
105
|
a) Determine the mean production of acorn in the last six years.
b) Calculate the standard deviation of data relative to acorn production.
c) Design the dispersion diagram and explain if we can conclude something about the relation between the annual production of acorn and the mean weight of pigs created in that farm property. Explain.
d) Calculate the correlation coefficient and explain it.