A bag contains 5 blacks balls and 3 red balls. Two balls are picked at random without replacement. What is the probability that a black and red balls are picked?
Black balls = 5
Red balls = 3
P(B) = \(\frac{5}{8}\), P(R) = \(\frac{3}{8}\)
P( a Black and a Red) = black ball and red ball or red ball and black ball i.e BR + RB
= (\(\frac{5}{8}\)) * (\(\frac{3}{7}\)) + (\(\frac{3}{8}\)) * (\(\frac{5}{7}\))
= (\(\frac{15}{56}\)) + (\(\frac{15}{56}\))
= \(\frac{30}{56}\)
= \(\frac{15}{28}\)
There is an explanation video available below.
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