Probability of amazon spinner

Question

• Find the probability of getting on Yamaha Guitar and Bose Speaker and BetterLuckNext time is after spinning the spinner in 10 times?

• Fine the probability of getting on 6 or 20 or Better Luck next time is after spinning the spinner in 25 times?

• Find the probability of getting on `Better luck next time is after spinning the spinner in 5 times

• Efforts:

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I mean like Imagine we are trying to get the probability of Amazon Spinner isn't that interesting?

Answer 1

By inclusion-exclusion principle, the first quantity should be

\begin{align} 1 - 3\left(\frac56 \right)^{10} + 3\left( \frac46\right)^{10}-\left( \frac12\right)^{10} \approx 0.5685 \end{align}

which agrees with the following simulation

from random import randrange

n = 10
trial_number = 100
choices = 6
success_count = 0
for t in range(trial_number):
    A = [0] * choices
    for i in range(n):
        A[randrange(choices)] += 1
    if A[0]*A[1]*A[2] > 0:
        success_count += 1
print(success_count/trial_number)