Question

isaiah has a bag full of colored marbles. he picks one marble at random, keeps it, and then picks another.
which of the following is an example of conditional probability?

the probability that the first marble isaiah picks is red and the second one is blue

the probability that the first marble isaiah picks is red or blue

the probability that neither of the marbles that isaiah picks is red

the probability that the second marble isaiah picks is blue given that the first marble is red

Explanation:

Conditional probability is the probability of an event occurring given that another event has already occurred. Let's analyze each option:

• The first option is the probability of two independent - like (but actually dependent here) sequential events without a "given" condition, so it's a joint probability, not conditional.
• The second option is the probability of a single event (first marble being red or blue), no condition involved.
• The third option is the probability of two events (neither marble is red) without a conditional statement.
• The fourth option has the phrase "given that the first marble is red", which means we are finding the probability of the second marble being blue under the condition that the first marble is red. This fits the definition of conditional probability.

Answer:

the probability that the second marble Isaiah picks is blue given that the first marble is red