Question

Consider the experiment: You have 30 marbles in a jar - 5 are red, 10 are blue, and 15 are yellow. You randomly pick one marble from the jar. Which of the following uses the complement rule to calculate the probability of not picking a blue marble?

a) P(not blue) = 1 - P(blue)
b) P(not blue) = P(blue) / P(total)
c) P(not blue) = P(blue) + P(yellow)
d) P(not blue) = P(total) - P(blue)

Answer 1

The correct answer for calculating the probability of not picking a blue marble using the complement rule is P(not blue) = 1 - P(blue). This is a direct application of the rule that the probability of an event's complement is 1 minus the probability of the event itself.

Step-by-step explanation:

The experiment described involves picking a marble from a jar with a total of 30 marbles of different colors. To calculate the probability of not picking a blue marble using the complement rule, one must identify the correct mathematical expression.

The complement rule states that the probability of an event not occurring is equal to 1 minus the probability of the event occurring. Therefore, if we let P(blue) represent the probability of drawing a blue marble, the probability of not drawing a blue marble is P(not blue) = 1 - P(blue). Hence, the correct answer is a) P(not blue) = 1 - P(blue).

An example that follows this concept would be if a bag contains three red marbles and seven blue marbles, the probability of not picking a red marble is 1 - (3/10) = 7/10, since there's a 3 in 10 chance of picking a red marble.

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