Grade 7 Math · Data

Probability of dependent events

Find the probability of two events happening one after another without replacement, where the second event's probability depends on the first. Unlimited questions, five difficulty levels, and a full worked solution every time, included free with weekly lessons.

Practice this skill Curriculum: G7-D2.1, G7-D2.2

Try one

A bag has 3 purple, 6 orange jelly beans. Two are drawn at random, one after another, without putting the first one back. What is the probability that both are orange?

Answer: 5/12

See one solved, step by step

A bag has 5 purple, 7 red marbles. Two are drawn at random, one after another, without putting the first one back. What is the probability that the first is red and the second is purple?

📘 Worked solution

1First draw: P(red) = 7127 out of 12 marbles are red.

2Removing one red leaves 11 total, but there are still 5 purple marbles.Only the count of the colour drawn changes -- the count of the other colour stays the same.

3Second draw: P(purple) = 511Use the new total for the second draw.

4(712) · (511) = 35132These draws are dependent -- multiply the two probabilities together.

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