Using a tree diagram, find the probability that exactly one head is obtained when two fair coins are tossed.

A fair six-sided spinner, $P$, has edges marked $0, 1, 2, 2, 3$ and $4 .$
A fair four-sided spinner, $Q$, has edges marked $0,-1,-1$ and $-2 .$

Each spinner is spun once and the numbers on which they come to rest are added together to give the score, $S$. Find:

$\mathrm{P}(S=2)$

A fair six-sided spinner, $P$, has edges marked $0, 1, 2, 2, 3$ and $4 .$
A fair four-sided spinner, $Q$, has edges marked $0,-1,-1$ and $-2 .$

Each spinner is spun once and the numbers on which they come to rest are added together to give the score, $S$. Find:

$\mathrm{P}\left(S^2=1\right)$

Letters and packages can take up to $2$ days to be delivered by Speedipost couriers. The following table shows the percentage of items delivered at certain times after sending.

Find the probability that when three letters are posted on Monday, none of them are delivered on Tuesday.

Letters and packages can take up to $2$ days to be delivered by Speedipost couriers. The following table shows the percentage of items delivered at certain times after sending.

Find the probability that when a letter and a package are posted together, the letter arrives at least $1$ day before the package.

The following histogram represents the results of a national survey on bus departure delay times.

Two buses are selected at random. Calculate an estimate of the probability that:

both departures were delayed by less than $4$ minutes

The following histogram represents the results of a national survey on bus departure delay times.

Two buses are selected at random. Calculate an estimate of the probability that:

at least one of the buses departed more than $7$ minutes late.

Praveen wants to speak on the telephone to his friend. When his friend's phone rings, he answers it with constant probability $0.6$. If Praveen's friend doesn't answer his phone, Praveen will call later, but he will only try four times altogether. Find the probability that Praveen speaks with his friend:

after making fewer than three calls