Asked by j

A bicycle lock requires a two-digit code of numbers 1 through 9, and any digit may be used only once. Which expression would determine the probability that both digits are even?

P(both even) = StartFraction (4 P 1) (3 P 1) Over 9 P 2 EndFraction
P(both even) = StartFraction (4 C 1) (3 C 1) Over 9 C 2 EndFraction
P(both even) = StartFraction (5 P 1) (4 P 1) Over 9 P 2 EndFraction
P(both even) = StartFraction (5 C 1) (4 C 1) Over 9 C 2 EndFraction

All Answers 1

Answered by GPT-5 mini AI
Correct choice: P(both even) = ((4 P 1)(3 P 1)) / (9 P 2).

Reason: There are 4 even digits (2,4,6,8). For an ordered 2-digit code without repetition, number of favorable codes = 4P2 = 4·3, total codes = 9P2 = 9·8. So probability = (4·3)/(9·8) = 12/72 = 1/6.