Independent and Dependent Events

Watch this lecture series to see more various examples of calculating probabilities of independent and dependent events. When the outcome of one event depends on the outcome of another, the events are considered dependent. Complete the interactive exercises

Practice

Probability with general multiplication rule - Questions

1. Ana is a teacher who plays a review game with her class. The game involves writing each student's name on an identical slip of paper and selecting students at random. Here's the makeup of her class:

\begin{array}{lccc}\text { Grade } & 9^{\text {th }} & 10^{\text {th }} & 11^{\text {th }} \\\hline \text { Number of students } & 12 & 9 & 7\end{array}

Suppose that Ana picks a name, replaces it, and picks a name again.

What is the probability that NEITHER of the students selected are 9^{\text {th }} graders?

Round your answer to two decimal places.

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2. An airport has an electronic system that randomly selects bags for extra security screening. Each bag has a 14 \% probability of being selected for extra screening, and one bag being selected or not doesn't affect whether or not another bag will be selected.

Suppose that 2 bags go through the system, one after the other.

What is the probability that both bags are selected for extra screening?

Round your answer to two decimal places.

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3. Hamid is playing a trivia game with multiple choice questions. Each question has 2 correct answers among 5 answer choices.

Hamid has no idea what the answers to a certain question are, so he needs to choose two different answers at random.

What is the probability that Hamid guesses both answers correctly?

Round your answer to two decimal places.

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4. Sammy and Hannah are finalists in a cooking competition. For the final round, each of them will randomly select a card without replacement that will reveal what their star ingredient must be. Here are the available cards:



Sammy and Hannah both want to get leeks as their star ingredient. Sammy will draw first, followed by Hannah.

What is the probability that NEITHER contestant draws leeks?

Round your answer to two decimal places.

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