# There are 5 orange books, 12 black books, and 8 tan books on Mr. Johnsons bookshelf. Calculate the p

Discussion in 'Calculator Requests' started by math_celebrity, Jun 29, 2019.

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There are 5 orange books, 12 black books, and 8 tan books on Mr. Johnsons bookshelf. Calculate the probability of randomly selecting a black book and then a tan book without replacement. Write your answer as a percent.

P(black book first draw)
P(black book first draw) = 12 black / (5 orange + 12 black + 8 tan)
P(black book first draw) = 12 / 25

P(tan book second draw)
P(tan book second draw) = 8 tan / (5 orange + 11 black + 8 tan) <-- 11 black because we already drew one black
P(tan book second draw) = 8 / 24
Using our fraction reduction calculator, this simplifies to 1/3

Since each draw is independent, we multiply both probabilities:
P(black book first draw, tan book second draw) = 12/25 * 1/3
P(black book first draw, tan book second draw) = 12/75
P(black book first draw, tan book second draw) = 16%