A coin is tossed twice and the four possible outcomes are assumed to be equally likely. If $E$ is the event 'both head and tail occurred' and $F$ is the event 'at most one tail is observed'. Find $P\left(E\right), P\left(F\right), P\left(E/F\right)$ and $P\left(F/E\right)$.

$70\%$ of the girls studying in a particular class of a particular school pass in mathematics, while $80\%$ of them pass in biology and $65\%$ pass in both the subjects. One of these girls is selected. Find the probability that she fails in both the subjects.

(Write answer in decimal form)

$70\%$ of the girls studying in a particular class of a particular school pass in mathematics, while $80\%$ of them pass in biology and $65\%$ pass in both the subjects. One of these girls is selected. If she passes in mathematics then the probability that she passes in biology is $\frac{k}{14}$. Hence, find the value of $k$.

$70\%$ of the girls studying in a particular class of a particular school pass in mathematics, while $80\%$ of them pass in biology and $65\%$ pass in both the subjects. One of these girls is selected. The probability that she passes in mathematics when it is given that she passes in biology is $\frac{k}{16}$. Hence, find the value of $k$.

The probability that a boy buys a ball is $0.2$ while the probability that he buys a bat is $0.3$. The probability that he buys a ball when it is given that he has already bought a bat is $0.4$. Find the probability that he buys both a ball and a bat. Find also the probability that he buys a bat when he has already bought a ball.

A die is thrown three times, and the sum of three numbers thrown is $15$. Find the chance that the first throw was a four.

A die is thrown three times. The probability of their sum is $15$ while the first throw is a $4$ is $\frac{1}{k}$, then find the value of $k$.

A die is thrown thrice. All the throws show even numbers. What is the probability to have a sum less than or equal to $8$ in $3$ throws.