GRE-Style: Probability with Conditions

GRE Quantitative · Axiom Academy

EXAMPLE GRE-Style: Probability with Conditions A "given that…" setup — apply to a two-category student population. A school has 100 students . Of these, 60 are seniors . 45 students total take calculus, and 30 of the seniors take calculus. A senior is selected at random. What is the probability that this senior takes calculus? Conditional probability formula: Read as "the probability of A , given that B has already happened." The condition B shrinks the universe you're choosing from. Nice work — you just applied the conditional probability formula to a "given that…" GRE setup. The word "given" changes the denominator: once you're told the outcome is a senior, the universe shrinks from all 100 students down to the 60 seniors. Use counts directly: skips converting to probabilities first — divide the overlap count by the condition count. Watch for the classic trap: is not the same as the unconditional . The GRE often plants the unconditional answer as a wrong choice. Any time a GRE question says "given that…" or "of those who…", it's signaling a conditional probability — shrink your universe to the condition first. Venn diagram of the 100 students

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