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A box contains 10 red balls and 15 green balls. Two balls are drawn in succession without replacement. What is the probability that, the first is red and the second is green? - Mathematics and Statistics

Sum

A box contains 10 red balls and 15 green balls. Two balls are drawn in succession without replacement. What is the probability that, the first is red and the second is green?

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Solution

Let A ≡ the event that the first ball drawn is red

and B ≡ the event that the second ball is drawn is green.

Since there are 10 red and 15 green balls,

P(A) = `10/(10 + 15) = 10/25`

Now, the first red ball is not replaced in the bag, therefore now we have 24 balls containing 15 green balls.

∴ probability of getting second green ball under the condition that first red ball is not replaced in the 15 bag

= `"P"("B"/"A")`

= `15/24`

∴ P(first ball is red and second ball is green) = P(A ∩ B)

= `"P"("A")*"P"("B"/"A")`

= `10/25 xx 15/24`

= `1/4`

Concept: Multiplication Theorem on Probability
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