A box contain 2 white and 3 blue identical balls. If two balls are picked at random, one after the other, without replacement, what is the probability of picking two balls of different colours?
\(\frac{5}{25}\)
\(\frac{7}{20}\)
\(\frac{3}{5}\)
\(\frac{2}{3}\)
\(\frac{5}{6}\)
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Let W and B represent white and blue balls respectively.
But without replacement, W=2/5 or 2/4 and B=3/5 or 3/4 respectively.
From the tree diagram, line one =WW, line two =WB, line three=BW and line four=BB.
Now, Probability of picking two balls of different colours.
This is specific. It can either be first white, second blue or first blue, second white.
This is line two and Three.
Therefore, P(one blue, one white)
=>(2/5*3/4)+(3/4*2/5)
=>6/20+6/20
=>12/20
=>3/4
Reference :Adu D. B (2004) Comprehensive Mathematics for Senior Secondary Schools (S.S. 1, 2 & 3) (Revised Edition) 25, 223-224. Surulere Lagos. A. Johnson Publishers LTD.
