Question 1: Probability of 7 After Discarding Top 10 Cards
Take a shuffled deck of 52 playing cards and throw the first top 10 cards in the bin. What is the probability that the new top card is a 7?
Input
A standard shuffled 52-card deck. First 10 cards are discarded.
Output
What is the probability that the next top card is a 7?
Select the answer that is closest.
Choices:
0.01
0.03
0.1
0.2
0.33
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Question 2: Coin Flip Uniformity
You flip a coin 3 times. What is the probability that the outcome is the same for all flips? So all Heads or all Tails.
Input
3 independent fair coin flips.
Output
Probability that all outcomes are the same.
Select the answer that is closest.
Choices:
0.1
0.25
0.5
0.75
0.9
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Question 3: Dice Pair Sum Even
You roll three dice. What is the probability that two of these dice sum to an even number?
Input
Three fair six-sided dice.
Output
Probability that any two dice sum to an even number.
Select the answer that is closest.
Choices:
0.7
0.8
0.9
0.95
1
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Question 4: Random Walk Time
A student leaves University (U) to walk home (H). It is a distance of four blocks in a straight line.
At each crossing, they toss a coin deciding whether to move forwards (Heads) or backwards (Tails). Note that from U they cannot go backwards in which case they stay there if they throw Tails.
If it takes 7 minutes to walk each block, what is the probability they will be home in more than 30 minutes?
Input
Random walk of 4 blocks with coin flip decisions.
Output
Probability of taking more than 30 minutes (i.e., more than 4 blocks x 7 = 28 min).
Select the answer that is closest.
Choices:
0.05
0.25
0.5
0.75
0.95
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Question 5: Even Sum of Five Dice
You roll five dice and sum their values. What is the probability that the sum is an even number?
Input
Five fair six-sided dice.
Output
Probability that total sum is even.
Select the answer that is closest.
Choices:
0.5
0.33
0.16
0.08
0.04
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