- 9.1 "The probability of being dealt a straight is 4/1000" means
that after a very large number of 5 card hands being dealt, approximately
.4% of them will have been a straight.
- 9.2 Probability gives information about what happens in the long
run, not what happens in a relatively small number of cases.
- 9.6
- a) Results vary. The true probability that the first head comes up
in an odd number of tosses is, .5+.5^3+.5^5+.5^7+... = 2/3.
- 9.7
- a) An impossible event has probability 0.
- b) A certain event has probability 1.
- c) A very unlikely event may have probability 0.01.
- d) An event that occurs more often than not may have
probability 0.6.
- 9.8
- a) Sample space is real numbers between 0 and 24.
- b) Sample space is values from $0.00 to $10.00 (or some other reasonable
upper bound for coins).
- c) Sample space is {A, B, C, D, F}.
- d) Sample space is {YY, YN, NY, NN}. (YY corresponds to a "yes" to the
question of whether or not the student took a math class in each of the two previous years.)
- 9.10
- a) The sample space is all possible weights of healthy adult
women. This might include numbers on the interval (85, 300).
- b) The sample space is all possible numbers of heart attacks
among the 11,000 physicians. This is an integer between 0 and 11000.
- c) The sample space is the possible number of broken eggs,
S= {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12}.
- 9.11 The probability of rolling a soft 4 is 2/36. The
probability of rolling any 4 is 3/36.
- 9.13 The probability that a tree dies is 1- (.686 + .256) = .058.
- 9.14 Model 1 is not legitimate since the probabilities of each
possible outcome do not add up to 1, that is, P(S) is not 1. Model 2 is
legitimate. Model 3 is not legitimate since the probabilities of each
possible outcome do not add up to 1. Model 4 is not legitimate since the
not all of the given probabilities are between 0 and 1.
- 9.17
- a) .4
- b) .6
- c) .2
- 9.18
- a) .5
- b) .5
- c) The probability that X is exactly equal to .5 is 0.
- 9.19
- a) The area of a triangle is 1/2 base times height. .5*2*1=1.
- b) P(Y<1) = .5.
- c) P(Y<.5) = .125.
- 9.21
| s | P{X=s} |
| 2 | 1/36 |
| 3 | 2/36 |
| 4 | 3/36 |
| 5 | 4/36 |
| 6 | 5/36 |
| 7 | 6/36 |
| 8 | 5/36 |
| 9 | 4/36 |
| 10 | 3/36 |
| 11 | 2/36 |
| 12 | 1/36 |
- 9.26
- a) 4176000/9094000 = .459 is the probability that a randomly
selected square kilometer of land in Canada is forested.
- b) 1- .459 = .541 is the probability that a randomly selected
square kilometer of land in Canada is not forested.
- 9.30
- a) The probability of drawing a blue candy is 0.1.
- b) The probability of not drawing a brown candy is 1 - 0.1 = 0.9.
- c) The probability of drawing a candy that is either yellow, orange,
or red is 0.2 + 0.1 + 0.2 = 0.5.
- 9.32
- a) Legitimate.
- b) Not legitimate. The probabilities do not add up to 1.
- c) Legitimate (if it is assumed that P(2)=P(3)=0).
- 9.35
- a) The possible arrangements are GGG, GGB, GBG, BGG, GBB, BGB, BBG, BBB
with each having a probability of 1/8.
- b) The probability of having 2 girls is 3/8. (P{X=2} = 3/8)
- c)
| i | P{X=i} |
| 0 | 1/8 |
| 1 | 3/8 |
| 2 | 3/8 |
| 3 | 1/8 |
- 9.43
- a) P{Y>300} = .5
- b) 370 is two standard deviations from the mean, so P{Y> 370} = .025.
(.05 is the probability of being further than two standard deviations from the mean
but in this case only one side is included.)
- 9.45
- a) The probability of matching exactly is 1/10000.
- b) The probability of matching in any order is (24/10,000).