A bag contains 3 red and 7 black balls.Two balls are selected at random one by one without replacement.what is the probability that they are alternate in colour ?
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Answer:
Step-by-step explanation:
Red =3
Black=7
Total=10
Let,P(A)= Probability that first is red.
P(B)=Probability that second is red:
Second is red ,There are 2 possible ways.
Either First is red and second is red.
Or First is black and Second is red.
So,
P(B)= (3c1/10 ×2c1/9 )+(7c1/10 ×3c1/9)
6/90 + 21/90
27/90
=0.3
Probability that first is red, given second is red.
P(A/B)
=P(A intersection B)/P(B).
=Probability that both first and second are red/Probability that second is red.
=(3c1/10 × 2c1/9)÷0.3
=6/90 ÷ 3/10
=6/90 × 10/3
=6/27
=2/9.
=0.2222
Hope it helps :)
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