MATHS - Statistics - Tree Diagrams

The video tutorial explains how to use tree diagrams to determine probabilities of multiple events. It covers the 'and' and 'or' rules for calculating probabilities, distinguishing between dependent and independent events. Examples include calculating the probability of Jack and Jess being on time and selecting counters of the same color from a bag. The tutorial emphasizes understanding the dependency of events to correctly apply probability rules.

What is the purpose of a tree diagram in probability?

• To show all possible outcomes of a single event

• To illustrate all possible outcomes of multiple events

• To display the sequence of events in a story

• To calculate the average of a set of numbers

In a tree diagram, when do you use the 'and' rule?

• When calculating the probability of neither event happening

• When calculating the probability of both events happening

• When calculating the probability of either event happening

• When calculating the probability of one event happening

What distinguishes a dependent tree diagram from an independent one?

• The second event is affected by the first in a dependent diagram

• The second event is unaffected by the first in a dependent diagram

• The first event is affected by the second in a dependent diagram

• Both events are unrelated in a dependent diagram

In the example of Jack and Jess, why is the question considered independent?

• Because Jack and Jess have the same probability of being late

• Because Jack's lateness affects Jess's probability

• Because both Jack and Jess are always on time

• Because Jack's lateness does not affect Jess's probability

How do you calculate the probability of only one person being on time in the Jack and Jess example?

• By adding the probabilities of both being late

• By multiplying the probabilities of both being on time

• By subtracting the probability of both being on time from 1

• By adding the probabilities of one being late and the other on time

In a dependent tree diagram, how does the probability change after the first event?

• The probability remains the same

• The probability increases

• The probability decreases

• The probability changes based on the outcome of the first event

In the dependent example with counters, what is the probability of drawing two counters of the same color?

• 54/110

• 4/11

• 27/55

• 7/11