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A random variable X takes the values 0, 1 and 2, with P(X = 0) = 29/100 and P(X = 1) = 13/100. Find P(X = 2).
X takes the values 0, 1, 2 with P(X = 0) = 25/100 and P(X = 1) = 15/100. Find P(X ≥ 1).
Which list could be the probabilities of a random variable with three values?
1. 0.1, 0.5 and 4/10
2. 0.5, 0.5 and 0.1
3. 0.8, 0.4 and −0.2
Which list could be the probabilities of a random variable with three values?
1. 0.2, 0.5 and 3/10
2. 0.5, 0.5 and 0.2
3. 0.8, 0.4 and −0.2
Which list could be the probabilities of a random variable with three values?
1. 0.4, 0.5 and 1/10
2. 0.5, 0.5 and 0.4
3. 0.8, 0.4 and −0.2
Which list could be the probabilities of a random variable with three values?
1. 0.3, 0.5 and 2/10
2. 0.5, 0.5 and 0.3
3. 0.8, 0.4 and −0.2
X takes the values 0, 1, 2 with probabilities 51/100, 15/100 and 34/100. Find E(X).
X = 1 with probability 7/10 and X = 0 otherwise. Find the standard deviation of X.
A game costs 1 dollar. You win 9 dollars (net) with probability 1/7; otherwise you lose your dollar. Find your expected net gain, in dollars.
A fair coin lands heads 7 times in a row. What is the probability of heads on the next toss?
1. 1/2: the coin has no memory
2. Less than 1/2: tails is due
3. More than 1/2: heads is on a streak
A fair coin lands heads 5 times in a row. What is the probability of heads on the next toss?
1. 1/2: the coin has no memory
2. Less than 1/2: tails is due
3. More than 1/2: heads is on a streak
A fair coin lands heads 10 times in a row. What is the probability of heads on the next toss?
1. 1/2: the coin has no memory
2. Less than 1/2: tails is due
3. More than 1/2: heads is on a streak
A fair coin lands heads 6 times in a row. What is the probability of heads on the next toss?
1. 1/2: the coin has no memory
2. Less than 1/2: tails is due
3. More than 1/2: heads is on a streak
A fair coin lands heads 8 times in a row. What is the probability of heads on the next toss?
1. 1/2: the coin has no memory
2. Less than 1/2: tails is due
3. More than 1/2: heads is on a streak
A fair coin lands heads 9 times in a row. What is the probability of heads on the next toss?
1. 1/2: the coin has no memory
2. Less than 1/2: tails is due
3. More than 1/2: heads is on a streak
What does it mean that the probability of rain tomorrow is 0.7?
1. On many days like tomorrow, it rains on about 70% of them
2. It will rain for 70% of the day
3. It will rain if the probability is above 0.5
What does it mean that the probability of rain tomorrow is 0.3?
1. On many days like tomorrow, it rains on about 30% of them
2. It will rain for 30% of the day
3. It will rain if the probability is above 0.5
What does it mean that the probability of rain tomorrow is 0.8?
1. On many days like tomorrow, it rains on about 80% of them
2. It will rain for 80% of the day
3. It will rain if the probability is above 0.5
What does it mean that the probability of rain tomorrow is 0.2?
1. On many days like tomorrow, it rains on about 20% of them
2. It will rain for 20% of the day
3. It will rain if the probability is above 0.5
What does it mean that the probability of rain tomorrow is 0.6?
1. On many days like tomorrow, it rains on about 60% of them
2. It will rain for 60% of the day
3. It will rain if the probability is above 0.5
What does it mean that the probability of rain tomorrow is 0.5?
1. On many days like tomorrow, it rains on about 50% of them
2. It will rain for 50% of the day
3. It will rain if the probability is above 0.5
What does it mean that the probability of rain tomorrow is 0.4?
1. On many days like tomorrow, it rains on about 40% of them
2. It will rain for 40% of the day
3. It will rain if the probability is above 0.5
To simulate a free throw made with probability 0.6 using random digits 0–9, how many of the ten digits should stand for 'made'?
12% of a population has a condition. A test is positive for 86% of people with the condition and for 11% of people without it. Find P(positive).
22% of a population has a condition. A test is positive for 81% of people with the condition and for 12% of people without it. Find P(condition | positive).
A disease affects 1 in 1,000 people. A test is 93% accurate for both sick and healthy people. Your test is positive. What is most likely?
1. You are still more likely healthy: false positives from the many healthy people outnumber the true positives
2. You are about 93% likely to be sick
3. You are certainly sick
A disease affects 1 in 1,000 people. A test is 99% accurate for both sick and healthy people. Your test is positive. What is most likely?
1. You are still more likely healthy: false positives from the many healthy people outnumber the true positives
2. You are about 99% likely to be sick
3. You are certainly sick
A disease affects 1 in 1,000 people. A test is 95% accurate for both sick and healthy people. Your test is positive. What is most likely?
1. You are still more likely healthy: false positives from the many healthy people outnumber the true positives
2. You are about 95% likely to be sick
3. You are certainly sick
A disease affects 1 in 1,000 people. A test is 98% accurate for both sick and healthy people. Your test is positive. What is most likely?
1. You are still more likely healthy: false positives from the many healthy people outnumber the true positives
2. You are about 98% likely to be sick
3. You are certainly sick
A disease affects 1 in 1,000 people. A test is 97% accurate for both sick and healthy people. Your test is positive. What is most likely?
1. You are still more likely healthy: false positives from the many healthy people outnumber the true positives
2. You are about 97% likely to be sick
3. You are certainly sick
A disease affects 1 in 1,000 people. A test is 92% accurate for both sick and healthy people. Your test is positive. What is most likely?
1. You are still more likely healthy: false positives from the many healthy people outnumber the true positives
2. You are about 92% likely to be sick
3. You are certainly sick
A disease affects 1 in 1,000 people. A test is 91% accurate for both sick and healthy people. Your test is positive. What is most likely?
1. You are still more likely healthy: false positives from the many healthy people outnumber the true positives
2. You are about 91% likely to be sick
3. You are certainly sick
A disease affects 1 in 1,000 people. A test is 96% accurate for both sick and healthy people. Your test is positive. What is most likely?
1. You are still more likely healthy: false positives from the many healthy people outnumber the true positives
2. You are about 96% likely to be sick
3. You are certainly sick
A disease affects 1 in 1,000 people. A test is 90% accurate for both sick and healthy people. Your test is positive. What is most likely?
1. You are still more likely healthy: false positives from the many healthy people outnumber the true positives
2. You are about 90% likely to be sick
3. You are certainly sick
A disease affects 1 in 1,000 people. A test is 94% accurate for both sick and healthy people. Your test is positive. What is most likely?
1. You are still more likely healthy: false positives from the many healthy people outnumber the true positives
2. You are about 94% likely to be sick
3. You are certainly sick

Answers

$\frac{29}{50}$
$\frac{3}{4}$
0.1, 0.5 and 4/10
$\frac{83}{100}$
$\frac{\sqrt{21}}{10}$
$\frac{3}{7}$
1/2: the coin has no memory
On many days like tomorrow, it rains on about 70% of them
$6$
$\frac{1}{5}$
$\frac{99}{151}$
You are still more likely healthy: false positives from the many healthy people outnumber the true positives