Topic 4.11: Conditional Probability Questions

In a class, 18 students study French and 7 of those also study German. A French student is chosen at random. Find the probability they also study German.

A climber on a staircase moves up one step with probability 0.6 and down one step with probability 0.4 at each move, independently. Let $S_n$ be the probability that the climber eventually reaches the top when standing on step $n$. For $n\ge 1$,

$S_n=0.4S_{n-1}+0.6S_{n+1}$.

Write down an expression for $S_3$ in terms of $S_2$ and $S_4$.

P(A ∩ B) = 0.35 and P(B) = 0.5. Find P(A | B).

$P(A\cap B)=0.35$ and $P(B)=0.5$. Find $P(A\mid B)$.

$P(A\mid B)=0.4$ and $P(B)=0.45$. Find $P(A\cap B)$.

P(A | B) = 0.4 and P(B) = 0.45. Find P(A ∩ B).

A survey records two events $A$ and $B$ with $P(A\mid B)=0.8$ and $P(B)=0.45$. Find $P(A\cap B)$.

A player has $n$ tokens. In each round the player wins one token with probability $0.3$ or loses one token with probability $0.7$. Let $Q_n$ be the probability of reaching $5$ tokens before running out, starting from $n$ tokens.

Write down an equation for $Q_2$ in terms of $Q_1$ and $Q_3$.

A frog sits on one of the lily pads numbered $0$ to $6$. Each jump takes it one pad to the right with probability $\frac{2}{5}$ or one pad to the left with probability $\frac{3}{5}$.

Let $T_n$ be the probability that it reaches pad $6$ before pad $0$, starting on pad $n$.

Write down $T_4$ in terms of $T_3$ and $T_5$.

P(A) = 0.7, P(B) = 0.4 and P(A ∪ B) = 0.85. Find P(A | B).

A two-way table shows 80 people: of 48 adults, 30 prefer tea; of 32 children, 8 prefer tea. Given a person prefers tea, find the probability they are an adult.

A bag has 5 red and 3 blue balls. Two are drawn without replacement. Given the first is red, find the probability the second is red.

Find $P(A\mid B)$ and $P(B\mid A)$.

$P(A)=0.7,P(B)=0.4$ and $P(A\cup B)=0.85$. Find $P(A\mid B)$.

A box holds 7 white and 5 black marbles. Two are taken without replacement. Given that the first is white, find the probability that the second is white.

A club has 60 members. Of these, 24 play tennis and 9 of those tennis players also play squash. A tennis player is chosen at random. Find the probability they play squash.

A game gives $P(A)=0.55$, $P(B)=0.4$ and $P(A\cup B)=0.75$. Find the probability of $A$ given that $B$ has happened.

A spinner has events $A$ and $B$ with $P(A\cap B)=0.24$ and $P(B)=0.6$. Find $P(A\mid B)$.

The random variable X follows a binomial distribution, X ~ B(18, 0.4).

Find P(X = 8 | X > 5).

The random variable X follows a binomial distribution, X ~ B(12, 0.35).

Find P(X = 5 | X > 3).