Amit M Agarwal Solutions for Chapter: Fundamentals of Probability, Exercise 5: Entrances Gallery

Four numbers are chosen at random (without replacement) from the set $\left\{1,2,3,\dots \dots ,20\right\}$

Statement I: The probability that the chosen numbers when arranged in some order will form an $AP$ is $\frac{1}{85}$.

Statement II: If the four chosen numbers form an $AP$, then the set of all possible values of common difference is $\left\{\pm 1,\pm 2,\pm 3,\pm 4,\pm 5\right\}$.

The probability that a leap year selected at random contains $53$ Sunday is

Three of the six vertices of a regular hexagon are chosen at random. The probability that the triangle with three vertices is equilateral, equals

A six faced unbiased die is thrown twice and sum of the numbers appearing on the upper face is observed to be $7$. The probability that the number $3$ has appeared at least once is

A bag has four pairs of balls of four distinct colours. If four balls are picked at random (without replacement), then the probability that there is at least one pair among them have the same colour, is

If $A$ and $B$ are two non-empty sets with $B^C$ denoting the complement of set $B$, such that $B\subset A$. Then, which of the following probability statements hold correct?

If birth to male child and birth to female child are equiprobable, then what is the probability that at least one of the three children born to a couple is male?

Two dice are tossed once, then the probability of getting an even number at the first die or at a total of $8$ is