$\color{#D61F06}{Colourful}$ Probability

Probability Level 3

A bag contains $6$ $\color{#D61F06} {\text{red}}$ and $3$ ${\text{white}}$ balls.Four balls are drawn out randomly one by one and are not replaced.What is the probability that they are alternatively of different colours?

$\textbf{Details and Assumptions}$

One such sequence may be: $\color{#D61F06} {\textbf{red}}$ , ${\textbf{white}}$ , $\color{#D61F06} {\textbf{red}}$ , ${\textbf{white}}$

If the probability can be expressed in the form $\dfrac{a}{b}$ where $a$ and $b$ are co prime integers then find $a+b$

The answer is 47.

1 solution

Aaaaa Bbbbb
Jan 24, 2015

The probability to choose based on additive and multiplex of probability principle. So We have: $P_{1}=Prob(Red|White|Red|White)=\frac{6}{9}*\frac{3}{8}*\frac{5}{7}*\frac{2}{6}$ $P_{2}=Prob(White|Red|White|Red)=\frac{3}{9}*\frac{6}{8}*\frac{3}{7}*\frac{6}{6}$ $P=P_{1}+P_{2}=\frac{5}{42}$ $a+b=\boxed{47}$

you have mistake in P2 .

P2 = ( 3/9 ) * ( 6/8 ) * ( 2 /7 ) * ( 5/6 )

Shohag Hossen - 5 years, 11 months ago

C o l o u r f u l \color{#D61F06}{Colourful} C o l o u r f u l Probability

The answer is 47.

1 solution

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$\color{#D61F06}{Colourful}$ Probability