Probability of Dependent Events

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 11 dependent probabilities with no item put back, like P(heart, heart) from a 52 card deck. The directions on the page read: No item is put back, so the second pick has one fewer item to choose from. Multiply to find each probability. Write it as a fraction in simplest form. 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.