NUMB3RS - Season 2 - "Mind Games" - Thumbs Up!

Algebra 2 / Pre-Calculus / Statistics

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Step 1•Multiple Choice

The Psychic's Probability

Let's first calculate the likelihood of the psychic's perfect failure. If the probability of incorrectly guessing a single card is p = 0.5, and each guess is independent, we can find the probability of guessing all 25 cards incorrectly using the multiplication rule for independent events:

$P(\text{All } 25 \text{ Wrong}) = 0.5^{25}$

Question:

What is the probability of guessing all 25 cards incorrectly by pure chance?

Hint: Calculate 0.5 raised to the power of 25. The answer will be written in scientific notation due to its extremely small size.

Monte Carlo Random Simulator

Modify the theoretical probability (for example, 0.3 for folding right-thumb, or 0.5 for card guesses) and run simulations of sample size n = 25. Compare actual data ranges to expected outcomes!

Probability (p):

Sample Size (n):

Number of Trials:

Simulated Distribution OutcomeMiddle 0.90 (Expected Range) Highlighted

Max Trials

Mid

Count 0: 0 trials

Count 1: 0 trials

Count 2: 0 trials

Count 3: 2 trials

Count 4: 3 trials

Count 5: 12 trials

Count 6: 17 trials

Count 7: 13 trials

Count 8: 21 trials

Count 9: 14 trials

Count 10: 7 trials

Count 11: 6 trials

Count 12: 4 trials

Count 13: 0 trials

Count 14: 1 trials

Count 15: 0 trials

Count 16: 0 trials

Count 17: 0 trials

Count 18: 0 trials

Count 19: 0 trials

Count 20: 0 trials

Count 21: 0 trials

Count 22: 0 trials

Count 23: 0 trials

Count 24: 0 trials

Count 25: 0 trials

Theoretical Mean:7.5

Normal Outliers Tail Cutoff:0.05 / 0.95