Exercises: Explain Conditional Probability and Independence in Everyday Language
Work through each section in order. This standard is about EXPLAINING in plain words, so several problems ask you to write complete sentences. Remember: "A given B" and "B given A" are different questions with different reference groups; "independent" means knowing one tells you nothing about the other (it is about information, not whether the events can happen together).
Warm-Up: Conditional and Independence Language
These problems review the plain-language meaning of conditioning and independence.
A news report says, "Among people who exercise daily, 80% sleep well." Which conditional probability does this claim describe?
A coach says, "Most professional basketball players are tall." Rewrite the claim with the condition REVERSED by filling each blank. "Most ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ people are ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ players." (First blank: tall or short. Second blank: a profession.)
Fluency Practice
Identify the conditioning, judge independence, and read the table.
An ad claims, "9 out of 10 dentists who tried our toothpaste recommend it." Which paraphrase correctly restates the conditioning?
A headline reads, "75% of people who tried the app kept using it." Which of the following is the UNCONDITIONAL "cousin" of this claim — a different, stronger statement about everyone?
A fair coin is flipped twice. Are the events "first flip is heads" and "second flip is heads" independent?
A roulette wheel has landed on red five times in a row. A gambler says, "Black is due now, so black is more likely on the next spin." Is the gambler right?
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