Venn Diagrams and Simple Probability

Front

What is a Venn Diagram?

Back

A Venn Diagram is a visual representation of the relationships between different sets, using overlapping circles to show commonalities and differences.

Front

Define probability.

Back

Probability is a measure of the likelihood that an event will occur, expressed as a number between 0 (impossible) and 1 (certain).

Front

What is the formula for calculating the probability of an event?

Back

The probability of an event A is calculated as P(A) = Number of favorable outcomes / Total number of outcomes.

Front

If a bag contains 3 red marbles, 4 green marbles, 2 blue marbles, and 1 yellow marble, how many total marbles are there?

Back

Total marbles = 3 + 4 + 2 + 1 = 10.

Front

What is the probability of pulling a red marble from the bag described?

Back

P(Red) = Number of red marbles / Total marbles = 3/10.

Front

What does 'with replacement' mean in probability?

Back

'With replacement' means that after an item is drawn, it is put back into the set before the next draw, keeping the total number of items constant.

Front

What is the probability of pulling a red marble and then a green marble with replacement?

Back

P(Red and Green) = P(Red) * P(Green) = (3/10) * (4/10) = 12/100.

Front

What does the intersection symbol (∩) represent in probability?

Back

The intersection symbol (∩) represents the event that two events occur at the same time.

Front

If a coin is flipped twice, what is the sample space?

Back

The sample space is {HH, HT, TH, TT}, where H = heads and T = tails.

Front

What is the probability of getting two heads when flipping a coin twice?

Back

P(Two Heads) = Number of favorable outcomes (HH) / Total outcomes = 1/4.