Question

An urn contains 7 white balls and 3 black balls. Two balls are selected at random without replacement. What is the probability :1 The first ball is black and the second ball is white.?

2: One ball is white and the other is black?

3:the two balls are white ?

Answer 1

An urn contains

• 7 white balls and
• 3 black balls

The total number of balls is therefore 10

We draw two balls without replacement

1.

P(the first ball is black and the second ball is white)

= P(the first ball is black) * P(the second ball is white/first ball is black)

= (3/10) * (7/9)

= 7/30

= 0.2333

2.

P(One ball is white and the other is black)

= P(the first ball is black) * P(the second ball is white/first ball is black) + P(the first ball is white ) * P(the second ball is black/first ball is white)

= (3/10 * 7/9)+(7/10*3/9)

=7/15

=0.4667

3.

P(Two balls are white)

= P(the first ball is white) * P(the second ball is white/first ball is white)

= 7/10 * 6/9

=7/15

=0.4667

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