I need some help with the following exercise:
Roll a die $7$ times. What is the probability: i) that the maximum value is $5$? ii) that the numbers $4, 5, 6$ each appear at least once?
I can't understand how to solve it. Thanks for your time.
2026-03-27 04:21:56.1774585316
Probability that if die is rolled seven times the maximum value is $5$; the numbers $4, 5, 6$ each appear at least once
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Hints
i) Find the probability that the max is less than $6$ and the probability that the max is less than $5$. Be aware that the second event is a subset of the first.
In mathematical language find: $$P(M\leq5)-P(M\leq4)$$ where $M$ denotes the maximum.
ii) Find the probability of the complement and apply inclusion/exclusion.
In mathematical language find:$$P(E_4\cup E_5\cup E_6)$$ where $E_i$ denotes the event that number $i$ is not thrown.