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.

	Same day	After $1$ day	After $2$ days
Letter	$40\%$	$50\%$	$10\%$
Package	$15\%$	$55\%$	$30\%$

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

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:

on the telephone on this occasion.

Each morning, Ruma randomly selects and buys one of the four newspapers available at her local shop. Find the probability that she buys:

the same newspaper on two consecutive mornings

Each morning, Ruma randomly selects and buys one of the four newspapers available at her local shop. Find the probability that she buys:

three different newspapers on three consecutive mornings.

In a group of five men and four women, there are three pairs of male and female business partners and three teachers, where no teacher is in a business partnership. One man and one woman are selected at random. Find the probability that they are:

both teachers