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Standard XII

Mathematics

Classical Definition of Probability

A box contain...

Question

A box contains $b$ blue balls and $r$ red balls. A ball is drawn randomly from the box and is returned to the box with another ball of the same colour. The probability that the second ball drawn from the box is blue is

\frac{b}{r + b}

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\frac{b^{2}}{(r + b)^{2}}

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\frac{b + 1}{r + b + 1}

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\frac{b (b + 1)}{(r + b) (r + b + 1)}

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Solution

The correct option is A $\frac{b}{r + b}$
$P (b_{2}) = P (b_{1}) \cdot P (\frac{b_{2}}{b_{1}}) + P (r_{1}) \cdot P (\frac{b_{2}}{r_{1}}) = \frac{b}{b + r} \cdot \frac{b + 1}{b + r + 1} + \frac{r}{b + r} \cdot \frac{b}{b + r + 1} = \frac{b^{2} + b + b r}{(b + r) (b + r + 1)} = \frac{b}{b + r}$

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A box contains b blue balls and r red balls. A ball is drawn randomly from the box and is returned to the box with another ball of the same colour. The probability that the second ball drawn from the box is blue is

The correct option is A br+bP(b2)=P(b1) ⋅P(b2b1)+P(r1) ⋅P(b2r1) =bb+r⋅b+1b+r+1 + rb+r⋅bb+r+1 =b2+b+br(b+r)(b+r+1) =bb+r

A box contains $b$ blue balls and $r$ red balls. A ball is drawn randomly from the box and is returned to the box with another ball of the same colour. The probability that the second ball drawn from the box is blue is

The correct option is A $\frac{b}{r + b}$
$P (b_{2}) = P (b_{1}) \cdot P (\frac{b_{2}}{b_{1}}) + P (r_{1}) \cdot P (\frac{b_{2}}{r_{1}}) = \frac{b}{b + r} \cdot \frac{b + 1}{b + r + 1} + \frac{r}{b + r} \cdot \frac{b}{b + r + 1} = \frac{b^{2} + b + b r}{(b + r) (b + r + 1)} = \frac{b}{b + r}$