A box contains 2 black, 4 white and 3 red balls. One ball is drawn at random from box and kept aside

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14.Probability

medium

A box contains $2$ black, $4$ white and $3$ red balls. One ball is drawn at random from the box and kept aside. From the remaining balls in the box, another ball is drawn at random and kept aside the first. This process is repeated till all the balls are drawn from the box. The probability that the balls drawn are in the sequence of $2$ black, $4$ white and $3$ red is

$\frac{1}{{1260}}$

$\frac{1}{{7560}}$

$\frac{1}{{126}}$

None of these

Solution

(a) The required probability

$ = \frac{2}{9} \times \frac{1}{8} \times \frac{4}{7} \times \frac{3}{6} \times \frac{2}{5} \times \frac{1}{4} \times 1 \times 1 \times 1 = \frac{1}{{1260}}$.

Standard 11

Mathematics

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medium

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A bag contains $3$ red and $5$ black balls and a second bag contains $6$ red and $4$ black balls. A ball is drawn from each bag. The probability that one is red and other is black, is

medium

Solution

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Two dice are thrown. The events $A, B$ and $C$ are as follows:

$A:$ getting an even number on the first die.

$B:$ getting an odd number on the first die.

$C:$ getting the sum of the numbers on the dice $\leq 5$

Describe the events $B$ or $C$