Question

what is the probability of drawing two blue marbles if the first marble is placed back in the bag before the second draw

Answer 1

We want to work out the probability of choosing a blue marble, and then choosing another blue marble:

P(choosing blue marble) and P(choosing blue marble)

in probability, and means times.

So

P(choosing blue marble) x P(choosing blue marble)

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In total there are 10 marbles, and 5 are blue. So the probability of choosing a blue marble is $\frac{5}{10}$

So:

P(choosing blue marble) x P(choosing blue marble)

= $\frac{5}{10}$ x $\frac{5}{10}$

= $\frac{25}{100}$        (this can simplify)

= $\frac{1}{4}$

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Answer

$\frac{1}{4}$