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WorksheetsThe Idea of Probability
Total questions: 13
Worksheet time: 7mins
I toss a penny and observe whether it lands heads up or tails up. Suppose the penny is fair, i.e., the probability of heads is 1/2 and the probability of tails is 1/2. This means that
every occurrence of a head must be balanced by a tail in one of the next two or three tosses.
if I flip the coin 10 times, it would be almost impossible to obtain 7 heads and 3 tails.
if I flip the coin many, many times the proportion of heads will be approximately 1/2, and this proportion will tend to get closer and closer to 1/2 as the number of tosses increases.
regardless of the number of flips, half will be heads and half tails.
all of the above.
There are two games involving flipping a fair coin. In the first game, you win a prize if you can throw between 45 percent and 55 percent heads; in the second game, you win if you can throw more than 60 percent heads. For each game, would you rather flip the coin 30 times or 300 times?
30 times for each game
300 times for each game
30 times for the first game, and 300 for the second
300 times for the first game, and 30 for the second
The outcomes of the games do not depend on the number of flips
If the individual outcomes of a phenomenon are uncertain, but there is nonetheless a regular distribution of outcomes in a large number of repetitions, we say the phenomenon is
random.
predictable.
uniform.
probable.
normal.
When two coins are tossed, the probability of getting two heads is 0.25. This means that
of every 100 tosses, exactly 25 will have two heads.
the odds against two heads are 4 to 1.
in the long run, the average number of heads is 0.25.
in the long run two heads will occur on 25% of all tosses.
if you get two heads on each of the first five tosses of the coins, you are unlikely to get heads the fourth time.
If I toss a fair coin 5000 times
and I get anything other than 2500 heads, then something is wrong with the way I flip coins.
the proportion of heads will be close to 0.5
a run of 10 heads in a row will increase the probability of getting a run of 10 tails in a row.
the proportion of heads in these tosses is a parameter
the proportion of heads will be close to 50.
You read in a book on poker that the probability of being dealt three of a kind in a five-card poker hand is 1/50. What does this mean?
If you deal thousands of poker hands, the fraction of them that contain three of a kind will be very close to 1/50.
If you deal 50 poker hands, then one of them will contain three of a kind.
If you deal 10,000 poker hands, then 200 of them will contain three of a kind.
A probability of 0.02 is somebody’s best guess for a probability of being dealt three of a kind.
It doesn’t mean anything, because 1/50 is just a number.
A basketball player makes 160 out of 200 free throws. We would estimate the probability that the player makes his next free throw to be
0.16.
50-50; either he makes it or he doesn’t.
0.80.
1.2.
80.
In probability and statistics, a random phenomenon is
something that is completely unexpected or surprising
something that has a limited set of outcomes, but when each outcome occurs is completely unpredictable.
something that appears unpredictable, but each individual outcome can be accurately predicted with appropriate mathematical or computer modeling.
something that is unpredictable from one occurrence to the next, but over the course of many occurrences follows a predictable pattern
something whose outcome defies description.
You are playing a board game with some friends that involves rolling two six-sided dice. For eight consecutive rolls, the sum on the dice is 6. Which of the following statements is true?
Each time you roll another 6, the probability of getting yet another 6 on the next roll goes down.
Each time you roll another 6, the probability of getting yet another 6 on the next roll goes up.
You should find another set of dice: eight consecutive 6’s is impossible with fair dice.
The probability of rolling a 6 on the ninth roll is the same as it was on the first roll.
None of these statements is true.
A poker player is dealt poor hands for several hours. He decides to bet heavily on the last hand of the evening on the grounds that after many bad hands he is due for a winner.
He's right, because the winnings have to average out.
He's wrong, because successive deals are independent of each other.
He's right, because successive deals are independent of each other.
He's wrong, because he’s clearly on a “cold streak.”
Whether he’s right or wrong depends on how many bad hands he’s been dealt so far.
Suppose you toss a fair coin ten times and it comes up heads every time. Which of the following is a true statement?
By the Law of Large Numbers, the next toss is more likely to be tails than another heads.
By the properties of conditional probability, the next toss is more likely to be heads given that ten tosses in a row have been heads.
Coins actually do have memories, and thus what come up on the next toss is influenced by the past tosses.
The Law of Large Numbers tells how many tosses will be necessary before the percentages of heads and tails are again in balance.
None of the above are true statements
In a game of roulette, the probability of landing on red is 18 out of 38. What does this imply about the expected outcomes over many spins?
It is guaranteed that red will come up more often than black.
None of the above statements are true.
Over a small number of spins, the outcomes will be evenly distributed between red and black.
In the long run, approximately 18 out of every 38 spins will land on red.
The probability of landing on red increases with each spin.
A student flips a fair coin 100 times and records the results. If they get 60 heads, what can be inferred about the fairness of the coin?
The student should flip the coin more times to get a better estimate of its fairness.
The coin is fair, as the results are just a random fluctuation.
None of these conclusions can be drawn from the results.
The coin is biased towards heads.
The results indicate that the coin is definitely unfair.
