Question

Chloe has 3 red pencils, 5 blue pencils, and 1 yellow pencil in her backpack. She chooses one pencil at random, puts it back, and then chooses another pencil .

The probability that Chloe chooses a blue pencil and then a red pencil is


The probability that Chloe chooses the yellow pencil and then a blue pencil is


No links please :)

Answer 1

A) P(chooses a blue pencil and then a red pencil) = 5/27

B) P(chooses yellow then blue) = 5/81

Explanation:

She has 3 red pencils, 5 blue pencils, and 1 yellow pencil in her backpack

Thus;

total number of pencils = 3 + 5 + 1 = 9 pencils

A) probability that she chooses a blue pencil and then a red pencil;

P(blue) = 5/9

Now she puts it bag after choosing which means the sum is back to 8 pencils.

Thus, if she now chooses a red pencil, then P(red) = 3/9 = 1/3

Thus;

P(chooses a blue pencil and then a red pencil) = 5/9 × 1/3

P(chooses a blue pencil and then a red pencil) = 5/27

B) probability that Chloe chooses the yellow pencil and then a blue pencil;

Similar to A above;

P(yellow) = 1/9

P(blue) = 5/9

P(chooses yellow then blue) = 1/9 × 5/9

P(chooses yellow then blue) = 5/81