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In an experiment, the probability that event occurs is and the probability that event occurs is .
If and are independent events, what is the probability that and both occur?
Simplify any fractions.

Ask by Huff Lynch. in Puerto Rico
Jan 23,2025

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The probability that both events and occur is .

Solución

To find the probability that both events and occur, we use the fact that if and are independent, the probability of both events happening together is the product of their individual probabilities.
Given:
  • Probability of ,
  • Probability of ,
The probability that both and occur is:
The fraction is already in its simplest form since 5 and 54 have no common divisors other than 1.
Answer:

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The Deep Dive

To find the probability that both independent events and occur, you multiply their probabilities together. The probability of event occurring is and the probability of event occurring is .
So, the combined probability :
Thus, the probability that both events and occur is .

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