A man draws a card from a pack of $52$ playing cards, replaces it and shuffles the pack. He continues this processes until he gets a card of spade. The probability that he will fail the first two times is
$\frac{9}{{16}}$
$\frac{1}{{16}}$
$\frac{9}{{64}}$
None of these
In a collection of tentickets, there are two winning tickets. From this collection, five tickets are drawn at random Let $p_1$ and $p_2$ be the probabilities of obtaining one and two winning tickets, respectively. Then $p_1+p_2$ lies in the interval
If $7$ dice are thrown simultaneously, then probability that all six digit appears on the upper face is equal to -
If $4 -$ digit numbers greater than $5,000$ are randomly formed from the digits
$0,\,1,\,3,\,5,$ and $7,$ what is the probability of forming a number divisible by $5$ when, the repetition of digits is not allowed ?
Fifteen persons among whom are $A$ and $B$, sit down at random at a round table. The probability that there are $4$ persons between $A$ and $B$, is
A committee of two persons is selected from two men and two women. What is the probability that the committee will have one man ?