More Tree Diagrams and Probability

Front

What is a tree diagram?

Back

A tree diagram is a graphical representation used to illustrate all possible outcomes of a sequence of events, showing the paths that can be taken based on different choices.

Front

What is the probability of an event?

Back

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

Front

How do you calculate the probability of picking two red counters without replacement?

Back

To calculate the probability of picking two red counters without replacement, use the formula: P(A and B) = P(A) * P(B|A). For example, P(first red) = 3/10, P(second red|first red) = 2/9, so P(both red) = (3/10) * (2/9) = 6/90.

Front

What is the probability of at least one event occurring?

Back

The probability of at least one event occurring can be calculated using the formula: P(at least one) = 1 - P(none).

Front

What is the formula for calculating the probability of independent events?

Back

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

Front

What does it mean for events to be mutually exclusive?

Back

Mutually exclusive events are events that cannot occur at the same time. The probability of either event occurring is the sum of their individual probabilities.

Front

How do you find the probability of rolling an even number on a die?

Back

The probability of rolling an even number (2, 4, or 6) on a standard die is calculated as: P(even) = number of even outcomes / total outcomes = 3/6 = 1/2.

Front

What is the significance of a probability of 0.5?

Back

A probability of 0.5 indicates that an event is equally likely to occur or not occur.

Front

How do you represent probabilities in a tree diagram?

Back

In a tree diagram, probabilities are represented along the branches, showing the likelihood of each outcome based on previous events.

Front

What is conditional probability?

Back

Conditional probability is the probability of an event occurring given that another event has already occurred, denoted as P(A|B).