Question

A jar contains 5 red chips, 3 blue chips, 6 white chips, and 10 green chips. Two chips are randomly drawn and not replaced.

What is the probability the chips drawn are red then blue.

Answer 1

To find the probability of drawing a red chip followed by a blue chip without replacement, we need to calculate the probability of each event separately and then multiply them together.

The probability of drawing a red chip on the first draw is:
P(red on first draw) = Number of red chips / Total number of chips
= 5 / (5 + 3 + 6 + 10)
= 5 / 24

After the first chip is drawn without replacement, there are now 23 chips left in the jar. The probability of drawing a blue chip on the second draw, given that the first chip was red and not replaced, is:
P(blue on second draw) = Number of blue chips / Remaining number of chips
= 3 / 23

To find the probability of both events occurring, we multiply the probabilities together:
P(red then blue) = P(red on first draw) * P(blue on second draw)
= (5 / 24) * (3 / 23)
= 15 / 552

Therefore, the probability of drawing a red chip followed by a blue chip without replacement is 15/552.