R D Sharma Solutions for Chapter: Probability, Exercise 5: VERY SHORT ANSWER QUESTIONS (VSAQs)

A single letter is selected at random from the word $\text{'}\mathrm{PROBABILITY}\text{'}$. What is the probability that it is a vowel?

What is the probability that a leap year will have $53$ Fridays or $53$ Saturdays?

Three dice are thrown simultaneously. If the probability of getting $15$ as the sum is $p$, then find the value of $108p$.

If the letters of the word $\text{'}\mathrm{MISSISSIPPI}\text{'}$ are written down at random in a row, what is the probability that four $\mathrm{S}\text{'}\mathrm{s}$ come together.

What is the probability that the $13\mathrm{th}$ day of a randomly chosen month is Friday?

Three of the six vertices of a regular hexagon are chosen at random. What is the probability that the triangle with these vertices is equilateral.

If ${\mathrm{E}}_1$ and ${\mathrm{E}}_2$ are independent events, write the value of $\mathrm{P}\left(\left({\mathrm{E}}_1\cup {\mathrm{E}}_2\right)\cap \left(\overline{E_1}\cap \overline{E_2}\right)\right)$.

If $\mathrm{A}$ and $\mathrm{B}$ are two independent events such that $\mathrm{P}(\mathrm{A}\cap \mathrm{B})=\frac{1}{6}$ and $\mathrm{P}(\overline{\mathrm{A}}\cap \overline{\mathrm{B}})=\frac{1}{3}$, then write the values of $\mathrm{P}\left(\mathrm{A}\right)$ and $\mathrm{P}\left(\mathrm{B}\right)$.