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Official 2019 Paper 2 · Q12

Paper 2Logic & proofProbability

Most students in a large college study Mathematics. A teacher chooses three different students at random, one after the other.

Consider these three probabilities:

R=P⁡(At least one of the students chosen studies Mathematics)S=P⁡(The second student chosen studies Mathematics)T=P⁡(All three of the students chosen study Mathematics)\begin{aligned} R&=\operatorname{P}(\text{At least one of the students chosen studies Mathematics})\\ S&=\operatorname{P}(\text{The second student chosen studies Mathematics})\\ T&=\operatorname{P}(\text{All three of the students chosen study Mathematics}) \end{aligned}

Which of the following is true?

AR<S<TR<S<T
BR<T<SR<T<S
CS<R<TS<R<T
DS<T<RS<T<R
ET<R<ST<R<S
FT<S<RT<S<R

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