A box contains 24 identical balls, of which 12 are white and 12 are black. balls are drawn at random

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14.Probability

easy

A box contains $24$ identical balls, of which $12$ are white and $12$ are black. The balls are drawn at random from the box one at a time with replacement. The probability that a white ball is drawn for the $4^{th}$ time on the $7^{th}$ draw is

$\frac{5}{{64}}$

$\frac{{27}}{{32}}$

$\frac{5}{{32}}$

$\frac{1}{2}$

(IIT-1994)

Solution

$P = {}^6{C_3} \times {\left( {\frac{1}{2}} \right)^3}\left( {\frac{1}{2}} \right){\rm{ }}\left( {\frac{1}{2}} \right) \Rightarrow P = \frac{5}{{32}}$.

Standard 11

Mathematics

The number of $3 \times 3$ matrices $A$ whose entries are either $0$ or $1$ and for which the system $\mathrm{A}\left[\begin{array}{l}\mathrm{x} \\ \mathrm{y} \\ \mathrm{z}\end{array}\right]=\left[\begin{array}{l}1 \\ 0 \\ 0\end{array}\right]$ has exactly two distinct solutions, is

hard

(IIT-2010)

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hard

(JEE MAIN-2017)

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medium

A bag contains $3$ white and $5$ black balls. If one ball is drawn, then the probability that it is black, is

normal

A box contains $24$ identical balls, of which $12$ are white and $12$ are black. The balls are drawn at random from the box one at a time with replacement. The probability that a white ball is drawn for the $4^{th}$ time on the $7^{th}$ draw is

Solution

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