APS Warm Up - Tree Diagrams 12-13-24

Front

What is a tree diagram?

Back

A tree diagram is a visual representation used to illustrate all possible outcomes of a probability experiment, showing the branching of each outcome.

Front

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

Back

Multiply the probabilities of each independent event. For example, if P(A) = 0.5 and P(B) = 0.4, then P(A and B) = P(A) * P(B) = 0.5 * 0.4 = 0.2.

Front

What is the probability of both Jim and Sue passing their driving test if the probability of each passing is 0.7?

Back

P(both pass) = P(Jim passes) * P(Sue passes) = 0.7 * 0.7 = 0.49.

Front

What is the probability of rolling two odd numbers with two dice?

Back

The probability of rolling an odd number on one die is 1/2. Therefore, P(both odd) = 1/2 * 1/2 = 1/4.

Front

What is the probability of only one of Jim or Sue passing the driving test?

Back

P(only one passes) = P(Jim passes) * P(Sue fails) + P(Jim fails) * P(Sue passes). If P(pass) = 0.7, then P(only one passes) = 0.7 * 0.3 + 0.3 * 0.7 = 0.42.

Front

What is the probability of drawing two blue counters from a bag containing 3 red and 7 blue counters without replacement?

Back

P(first blue) = 7/10, P(second blue) = 6/9. Therefore, P(both blue) = (7/10) * (6/9) = 42/90 = 14/30 = 7/15.

Front

If Jane has a 20% chance of winning a chess game, what is the probability she wins both games if she plays two?

Back

P(wins both) = P(win first) * P(win second) = 0.2 * 0.2 = 0.04.

Front

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

Back

P(Event) = Number of favorable outcomes / Total number of possible outcomes.

Front

What does 'without replacement' mean in probability?

Back

'Without replacement' means that once an item is drawn from a set, it is not returned to the set before the next draw, affecting the total number of items available.

Front

What is the difference between independent and dependent events in probability?

Back

Independent events do not affect each other's outcomes, while dependent events do; the outcome of one event influences the outcome of another.