For independent events ${A_1},\,{A_2},\,..........,{A_n},$ $P({A_i}) = \frac{1}{{i + 1}},$ $i = 1,\,\,2,\,......,\,\,n.$ Then the probability that none of the event will occur, is
$\frac{n}{{n + 1}}$
$\frac{{n - 1}}{{n + 1}}$
$\frac{1}{{n + 1}}$
None of these
An experiment involves rolling a pair of dice and recording the numbers that come up. Describe the following events:
$A:$ the sum is greater than $8$,
$B : 2$ occurs on either die
$C:$ the sum is at least $ 7$ and a multiple of $3.$
Which pairs of these events are mutually exclusive ?
The probability of obtaining sum ‘$8$’ in a single throw of two dice
From a book containing $100$ pages, one page is selected randomly. The probability that the sum of the digits of the page number of the selected page is $11$, is
If the probabilities of boy and girl to be born are same, then in a $4$ children family the probability of being at least one girl, is
Two dice are thrown. The probability that the sum of the points on two dice will be $7$, is