Tree Diagrams Practice Questions

Complete the probability tree diagram.

Work out the probability that Rosa wins both games.

A bag contains $5$ red counters and $3$ blue counters.

Kim takes at random a counter from the bag. She does not put the counter back in the bag.

She then takes at random a second counter from the bag.

Kim draws this probability tree diagram.

The diagram is not correct.

Write down two things that are wrong with the probabilities in the probability tree diagram.

Draw a probability tree diagram to show this information.

Work out the probability that the two chocolates Ramona eats are the same type of chocolate.

Work out the probability that at least one of the two bulbs fails within the first $1000$ hours of use.

You may use a probability tree diagram to help you.

State an assumption you have made in working out your answer to part (a).

In a game at a fair, a player throws a beanbag at a target twice.

The probability that the beanbag hits the target on any throw is $0.35$

The two throws are independent.

On Saturday the game is played $400$ times.

Work out an estimate for the number of times the target is hit exactly once.

Complete the probability tree diagram.

Work out the probability that the spinner lands on the same colour on both spins.

Every morning Dev drives past two sets of traffic lights on his way to work.

The probability that he is stopped at the first set of lights is $0.3$

If he is stopped at the first set of lights, the probability that he is stopped at the second set of lights is $x$

If he is not stopped at the first set of lights, the probability that he is stopped at the second set of lights is $0.5$

The probability that Dev is stopped at exactly one of the two sets of lights is $0.44$

Work out the value of $x$.

Work out the probability that all three batteries Asha takes are dead.

Work out the probability that exactly one of the three batteries Asha takes is dead.

You may use a probability tree diagram to help you.