Five cards numbered 1, 2, 3, 4 and 5 are in a hat. Two cards are drawn together (without replacement). What is the probability that the sum of the two numbers is even?

\frac{3}{5}

Correct answerYour answer

\frac{1}{2}

Correct answerYour answer

\frac{13}{25}

Correct answerYour answer

\frac{2}{5}

Correct answerYour answer

Show the answer and explanation

CorrectNot quiteAnswer D

Correct answer: D

Pairs possible: ${}^{5}C_{2} = 10$ .
An even sum needs two odd cards (from 1, 3, 5: 3 pairs) or two even cards (2 and 4: 1 pair).
Probability $= \frac{3 + 1}{10} = \frac{2}{5}$ .

Worth noting

$\frac{13}{25}$ is the answer if the first card is put back, since then a card can pair with itself. $\frac{1}{2}$ assumes odd and even sums are equally likely; with three odd cards and two even, they are not.

Concept: Even sum from odd-odd or even-even pairs
Typical timeTypical: 70 s
Your timeYours: —

The rule this testsBasic probability

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Ten questions from Counting and Basic Probability, at your own pace.

Five cards numbered 1, 2, 3, 4 and 5 are in a hat. Two cards are drawn together (without replacement). What is the probability that the sum of the two numbers is even?

Explanation