A box has $4$ red, and $3$ black marbles. Four marbles are picked up randomly. Find the probability that, $C =$ all the marbles are black.

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Solution

There are $7$ marbles. Out of these $4$ marbles can be drawn in $^{7} C_{4} = 35$ ways
$∴ n (S) = 35$
$C$ is an event of getting all marbles black.
$∵ 4$ black marbles cannot be drawn out of $3$ black ones. So, $C$ is an impossible event.
$∴ P (C) = 0$

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A box has 4 red, and 3 black marbles. Four marbles are picked up randomly. Find the probability that, C= all the marbles are black.

There are 7 marbles. Out of these 4 marbles can be drawn in 7C4=35 ways ∴n(S)=35C is an event of getting all marbles black.∵4 black marbles cannot be drawn out of 3 black ones. So, C is an impossible event.∴P(C)=0

A box has $4$ red, and $3$ black marbles. Four marbles are picked up randomly. Find the probability that, $C =$ all the marbles are black.

There are $7$ marbles. Out of these $4$ marbles can be drawn in $^{7} C_{4} = 35$ ways
$∴ n (S) = 35$
$C$ is an event of getting all marbles black.
$∵ 4$ black marbles cannot be drawn out of $3$ black ones. So, $C$ is an impossible event.
$∴ P (C) = 0$