Probability - Addition Rule

Front

What is the Addition Rule in probability?

Back

The Addition Rule states that the probability of the occurrence of at least one of two events is equal to the sum of their individual probabilities minus the probability of their intersection. Mathematically, it is expressed as: P(A or B) = P(A) + P(B) - P(A and B).

Front

If a box contains 18 blue flashlights, 3 red flashlights, 7 silver flashlights, and 2 black flashlights, what is the probability of selecting a blue or black flashlight?

Back

The total number of flashlights is 30. The number of favorable outcomes (blue + black) is 20. Therefore, the probability is P(blue or black) = \frac{20}{30} = \frac{2}{3}.

Front

What is the probability of spinning purple or green on a spinner with 6 equal sections?

Back

If the spinner has 6 equal sections and 2 of them are purple or green, the probability is P(purple or green) = \frac{2}{6} = \frac{1}{3}.

Front

What is the probability of landing on an odd number or a number divisible by 3 when spinning a spinner numbered 1 to 10?

Back

The odd numbers are 1, 3, 5, 7, 9 (5 outcomes) and the numbers divisible by 3 are 3, 6, 9 (3 outcomes). The overlap (3 and 9) counts as 2. Therefore, P(odd or divisible by 3) = \frac{5 + 3 - 2}{10} = \frac{6}{10} = \frac{3}{5}.

Front

What is the probability of rolling a 4 or an odd number on a seven-sided die?

Back

The odd numbers are 1, 3, 5, 7 (4 outcomes) and the number 4 (1 outcome). The total favorable outcomes are 5. Therefore, P(4 or odd) = \frac{5}{7}.

Front

If a box contains 18 blue chips, 6 red chips, 4 green chips, and 2 yellow chips, what is the probability of selecting a blue or yellow chip?

Back

The total number of chips is 30. The number of favorable outcomes (blue + yellow) is 20. Therefore, the probability is P(blue or yellow) = \frac{20}{30} = \frac{2}{3}.

Front

What is the formula for calculating the probability of two mutually exclusive events?

Back

For mutually exclusive events A and B, the probability is calculated as: P(A or B) = P(A) + P(B).

Front

How do you calculate the probability of two independent events occurring?

Back

For independent events A and B, the probability of both occurring is calculated as: P(A and B) = P(A) * P(B).

Front

What is the probability of drawing a red card or a face card from a standard deck of cards?

Back

There are 26 red cards and 12 face cards in a deck of 52 cards. The overlap (red face cards) is 6. Therefore, P(red or face) = \frac{26 + 12 - 6}{52} = \frac{32}{52} = \frac{8}{13}.

Front

What is the probability of rolling a sum of 7 with two dice?

Back

The possible combinations to roll a sum of 7 are (1,6), (2,5), (3,4), (4,3), (5,2), (6,1) which gives 6 favorable outcomes. The total outcomes with two dice are 36. Therefore, P(sum of 7) = \frac{6}{36} = \frac{1}{6}.