200k views
23 votes
In a bag, there are six white balls and four black balls. I take out two balls at random, one at a time, without replacement. What is the probability that the second ball I take is black

User Perpil
by
6.1k points

1 Answer

5 votes

Answer:


Probability = 0.4

Explanation:

Given


White = 6


Black = 4

Required

Probability that second is black

This selection can be represented as:

(Black and Black) or (White and Black)

The probability of Black and Black is:


P(Black\ Only) = (Black)/(Total) * (Black - 1)/(Total - 1)

1 is subtracted from the second fraction because it is probability without replacement


P(Black\ Only) = (4)/(10) * (4- 1)/(10 - 1)


P(Black\ Only) = (4)/(10) * (3)/(9)


P(Black\ Only) = (2)/(5) * (1)/(3)


P(Black\ Only) = (2)/(15)

The probability of White and Black is:


P(Black\ and\ White) = (Black)/(Total) * (White)/(Total - 1)

1 is subtracted from the second fraction because it is probability without replacement


P(Black\ and\ White) = (4)/(10) * (6)/(10- 1)


P(Black\ and\ White) = (4)/(10) * (6)/(9)


P(Black\ and\ White) = (2)/(5) * (2)/(3)


P(Black\ and\ White) = (4)/(15)

So, the required probability is:


Probability = P(Black\ Only) + P(Black\ and\ White)


Probability = (2)/(15) + (4)/(15)


Probability = (2+4)/(15)


Probability = (6)/(15)


Probability = 0.4

User Mikko Wilkman
by
7.3k points