General Addition Rule of Probability

Front

What is the General Addition Rule of Probability?

Back

The General Addition Rule states that for any two events A and B, the probability of A or B occurring is given by: P(A ∪ B) = P(A) + P(B) - P(A ∩ B).

Front

How do you calculate the probability of spinning purple or green on a spinner with 6 equal sections?

Back

To find the probability of spinning purple or green, count the favorable outcomes (e.g., 2 sections) and divide by the total outcomes (6). P(purple or green) = \frac{2}{6} = \frac{1}{3}.

Front

What is the probability of choosing a king or a club from a standard deck of 52 cards?

Back

There are 4 kings and 13 clubs, but one king is also a club. Using the General Addition Rule: P(king or club) = P(king) + P(club) - P(king and club) = \frac{4}{52} + \frac{13}{52} - \frac{1}{52} = \frac{16}{52}.

Front

What is the probability of choosing a card that is a spade or a 7?

Back

There are 13 spades and 4 sevens, but one of the sevens is a spade. Using the General Addition Rule: P(spade or 7) = P(spade) + P(7) - P(spade and 7) = \frac{13}{52} + \frac{4}{52} - \frac{1}{52} = \frac{16}{52}.

Front

If a jar contains 2 pink, 6 red, and 4 blue marbles, what is the probability of picking a red or blue marble?

Back

Total marbles = 2 + 6 + 4 = 12. Favorable outcomes (red or blue) = 6 + 4 = 10. P(red or blue) = \frac{10}{12} = \frac{5}{6}.

Front

What is the probability of spinning green or blue on a spinner with 12 equal sections?

Back

Assuming 5 sections are green and 2 are blue, P(green or blue) = \frac{5 + 2}{12} = \frac{7}{12}.

Front

Define mutually exclusive events in probability.

Back

Mutually exclusive events are events that cannot occur at the same time. For example, when flipping a coin, getting heads and tails are mutually exclusive.

Front

What is the probability of an event that is certain to happen?

Back

The probability of an event that is certain to happen is 1 (or 100%).

Front

What is the probability of an event that is impossible?

Back

The probability of an event that is impossible is 0.

Front

Explain the concept of independent events in probability.

Back

Independent events are events where the occurrence of one event does not affect the occurrence of another. For example, flipping a coin and rolling a die are independent events.