With or Without Replacement

Start with Independent or Dependent and With or Without Replacement. Move to the probability sheets once students can label each situation, and use the review as a final check.

Find the probability of a second pick with and without replacement, like 12 red and 8 blue marbles. The directions on the page read: After the first pick, find the probability of the second pick as a fraction in simplest form. Circle I if the events are independent or D if they are dependent. The page opens with a worked example, and an answer key is included.

Yes, both. We made it for 8th grade probability, and it works the same at home or at school. At home, a student can work through it alone and then go over it with you, which shows quickly what is solid and what needs another look. In class it works as independent practice, homework or a warm-up, and you can print one copy or a full set.

Ask whether the first event changes the chances of the second. Picking a card and keeping it out makes the second pick dependent. Rolling a number cube twice does not.

Multiply the two probabilities. For 2 red and 5 blue marbles with the first put back, P(red, red) is 2/7 times 2/7, which is 4/49.

The second pick has one fewer item, and the count of the picked color drops by one. For 7 gold and 5 silver coins with a gold kept out, the next P(gold) is 6/11.

Yes. Each of the 10 independent and dependent events sheets comes with an answer key.