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?
A
\(\frac{15}{28}\)
B
\(\frac{13}{28}\)
C
\(\frac{5}{14}\)
D
\(\frac{3}{14}\)
Verified Correct Answer: A.
Step-by-Step Mathematical Solution
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
= (\(\frac{5}{8}\)) * (\(\frac{3}{7}\)) + (\(\frac{3}{8}\)) * (\(\frac{5}{7}\))
= (\(\frac{15}{56}\)) + (\(\frac{15}{56}\))
= \(\frac{30}{56}\)
= \(\frac{15}{28}\)
Source: Myschool Past Questions Archive (Record #7846)