Question

A bag contain 5white,7red and 3 black balls.If three balls are drawn one by one without replacement,find the probability that none is red?

Answer 1

Hi there!
Here's the answer:

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In the bag,
5 - white
7 - red
3 - black

Total no. of balls= 15.

Now,
To find probability that none is red,
we have to choose 3 balls other than red ball but note that balls are not replaced.

Probability = n(E) / n(S)
= (no. of non red coloured balls) / (total no. of balls)

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Probability of drawing the first ball that is not red: (P1)::

Here n(E)= 8C1 & n(S) = 15C1

•°• Probability P1= 8/15

(Now, as ball is not replaced
no. of non red colored balls => 7 and total balls= 14)

Probability of drawing the Second ball that is not red: (P2)::

Here n(E)= 7C1 & n(S) = 14C1

•°• Probability P2= 7/14

Now, as ball is not replaced
no. of non red colored balls => 6 and total balls= 13)

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Probability of drawing the Third ball that is not red: (P1)::

Here n(E)= 8C1 & n(S) = 15C1

•°• Probability P1= 8/15

(Now, as ball is not replaced
no. of non red colored balls => 6 and total balls= 13)

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Probability of drawing Second ball of not red: (P2)::

Here n(E)= 6C1 & n(S) = 13C1

•°• Probability P3 = 6/13

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Now,
Probability that none is red = P1 × P2 × P3
= (8/15) × (7/14) × (6/13)
= 8/65

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:)
Hope it helps