A bag has 5 red and 3 blue balls. 2 balls are drawn at random together. What is the probability that both are red?

\frac{5}{28}

Correct answerYour answer

\frac{5}{14}

Correct answerYour answer

\frac{25}{64}

Correct answerYour answer

\frac{5}{8}

Correct answerYour answer

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CorrectNot quiteAnswer B

Correct answer: B

Ways to choose 2 of the 8 balls: ${}^{8}C_2 = 28$ . Ways to choose 2 of the 5 red: ${}^{5}C_2 = 10$ .
So the probability is $\frac{10}{28} = \frac{5}{14}$ .

Worth noting

$\frac{25}{64} = \left(\frac{5}{8}\right)^2$ multiplies as if the first ball went back before the second; drawn together, it does not.

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Explanation