Question

A bag contains 5 red balls &7black balls . if 1 ball is drawn at random.find the probability that it's black ball,red ball ¬ green

Answer 1

As it's not clearly specified whether the ball drawn is with replacement or without replacement, so we can have two cases in this question .

Case 1:

Let's consider that balls are drawn with replacement .

Let A denotes the event that two balls of the same color are drawn.

B denotes the event that both the balls are white .

C denotes the event that both the balls are black.

So now Probability of A ie P(A) =P(B) + P(C).

Let's look at the basic formula of probability ie No of favorable outcome / Total outcomes

Now , P(B) = 5/8X5/8 ie 25/64 as this is the case of with replacement ie. probability of drawing a white ball multiplied by the probability that second ball is white given that first ball was white .

Probability of drawing a white ball is 5/8 and the second white ball is also 5/8.

Similarly P(C) =3/8X3/8=9/64 .

Therefore , P(A)=34/64.

Case 2

Balls are drawn without replacement .

Keeping all the events same .

So now P(B)= 5/8X4/7=20/56

P(C)= 3/8X2/7=6/56.

P(A)=26/56.

PS: One must be clear about the difference between “or” and “ and”P(AorB)=P(AUB)P(AandB)=P(ANB).

Answer 2

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It is proper