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A home-schooled student is experimenting with dice in a probability lab. They roll a fair 6-sided die four times. What is the probability that exactly two of the rolls show a prime number?
We want exactly 2 primes in 4 rolls — binomial distribution:
A space agriculture designer is configuring a seed dispenser that randomly selects one of 8 plant varieties each time it activates. If the dispenser operates 5 times independently, what is the probability that exactly two different varieties are selected, with one appearing exactly three times?

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