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

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:

in a business partnership with each other

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:

each in a business partnership but not with each other.

A biased die in the shape of a pyramid has five faces marked $1, 2, 3, 4$ and $5$ . The possible scores are $1, 2, 3, 4$ and $5$ and $\mathrm{P}\left(x\right)=\frac{k-x}{25}$, where $k$ is a constant.

Find, in terms of $k$, the probability of scoring $5$.

A biased die in the shape of a pyramid has five faces marked $1, 2, 3, 4$ and $5$ . The possible scores are $1, 2, 3, 4$ and $5$ and $\mathrm{P}\left(\mathrm{x}\right)=\frac{k-x}{25}$, where $k$ is a constant.

Find, in terms of $k$, the probability of scoring less than $3$ .