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RV-16-001 · Two-way table: conditional selection without replacement

A survey records how students travel and whether they attend a club.
WalkBus
Club1811
No club1520

(a) A club member is selected at random. Find the probability that this student walks.

(b) Two students are selected at random without replacement from the whole survey. Find the probability that both travel by bus.

Part (a) Two-Way Tables: Conditional & Without-Replacement Probability Booklet p. 60 & p. 62
Method
1) Restrict denominator to Club row total for part (a)
2) For part (b) without replacement: multiply (Bus / Total) × ((Bus −
1) / (Total − 1))
Worked Example (RV-16-001 · Part (a))
A club member is selected at random. Find the probability that this student walks.
1)
Restrict the denominator to the 29 club members.
2)
1829\frac{18}{29}
Ans = 1829\frac{18}{29}
Part (b) Two-Way Tables: Conditional & Without-Replacement Probability Booklet p. 60 & p. 62
Method
1) Restrict denominator to Club row total for part (a)
2) For part (b) without replacement: multiply (Bus / Total) × ((Bus −
1) / (Total − 1))
Worked Example (RV-16-001 · Part (b))
Two students are selected at random without replacement from the whole survey. Find the probability that both travel by bus.
1)
3164\frac{31}{64}
2)
1021\frac{10}{21}
3)
155672\frac{155}{672}
Ans = 155672\frac{155}{672}