Probability

Find the probability that all three cars are the same colour.

Find the probability that, when the 3 cars are selected, at least one car is white and at least one car is black.

Find the probability that both marbles selected are the same colour.

Find the probability that the first marble is blue given that the second marble is red.

Draw a tree diagram to represent this information, giving the probability on each branch.

Find the probability that both marbles chosen are the same colour.

Find the probability that the marble chosen from bag $A$ is blue, given that the marble chosen from bag $B$ is blue.

Draw a tree diagram to illustrate this information, showing all the probabilities.

Find the probability that a randomly chosen student who applies to Drydale College is accepted.

Find the probability that a randomly chosen student who applies to Drydale College takes at least two tests given that the student is accepted.

Three friends apply to Drydale College.

Find the probability that all three are rejected.

Complete the tree diagram below by entering all the remaining outcomes and probabilities.

Find the probability that all three marbles chosen are the same colour.

Write down an equation in terms of $x$ and hence find the value of $x$.

Find the probability that the two cards have pictures of the same type of vehicle on them.

Draw a fully labelled tree diagram to illustrate this information, including all the probabilities.

Find the probability that one red marble and one blue marble are obtained.

Find the probability that a white counter is chosen from box $A$, given that one red marble and one blue marble are obtained.

Draw a tree diagram to represent this information, showing all the probabilities.

Find the probability that the two discs that Priti chooses are blue.

Find the probability that the two discs that Priti chooses come from bag $X$ given that at least one of the discs is red.

Find the probability that both the marbles chosen are red.

Find the probability that the first marble chosen is blue given that the second marble chosen is red.

Draw up the probability distribution table for $X$.

Harry has two other coins, each of which is biased so that the probability of obtaining a head when it is thrown is $p$. He throws all five coins at the same time. The random variable $Y$ is the number of heads that he obtains.

Given that $\text{P}(Y = 0) = 6\text{P}(Y = 5)$, find the value of $p$.