1. Dr. Stats plans to toss a fair coin 10,000 times in the hope that it will lead him to a deeper understanding of the laws of probability. Which of the following statements is true?
A) It is unlikely that Dr. Stats will get more than 5,000 heads.
B) Whenever Dr. Stats gets a string of 15 tails in a row, it becomes more likely that the next toss will be a head.
C) The fraction of tosses resulting in heads should be close to ½.
D) The chance that the 100th toss will be a head depends somewhat on the result of the first 99 tosses.
E) All of the above statements are true.
2. There are 2,598,960 possible 5-cards hands that can be dealt from an ordinary 52-card deck. Of these 5,148 have all five cards of the same suit. (In poker such hands are called flushes.) The probability of being dealt such a hand (assuming randomness) is closest to:
A) 1/4
B) 1/10
C) 1/100
D) 1/500
E) 1/1000
The casino game craps is based on rolling two dice. Here is the assignment of probabilities to the sum of numbers on the up face when two dice are rolled:
|
Outcome
|
2
|
3
|
4
|
5
|
6
|
7
|
8
|
9
|
10
|
11
|
12
|
|
Probability
|
1/36
|
2/36
|
3/36
|
4/36
|
5/36
|
6/36
|
5/36
|
4/36
|
3/36
|
2/36
|
1/36
|
3. Gigi has rolled a natural on four straight tosses of the dice. This excites the gamblers standing around the table. They should know that:
A) Gigi has a hot hand, so she is more likely to roll another natural.
B) The law of averages says that Gigi is now less likely to roll another natural.
C) Rolls are independent, so the chance of rolling another natural has not changed.
D) Four straight naturals are almost impossible, so the dice are probably loaded.
E) They should not be surprised because the probability of four straight naturals is 2/36.