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Probability — MATHS STD 12 Science — Question

Rajasthan BoardEnglish MediumSTD 12 ScienceMATHSProbability3 Marks
Question
Probality of solving specific problem independently by $A$ and $B$ are $\frac{1}{2}$ and $\frac{1}{3}$ respectively. If both try to solve the problem independently. Find the probability that the problem is solved.
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Answer

Given: $P(A)=1 / 2, \quad P(B)=1 / 3$
$\therefore$ Probability of NOT solving:
$P\left(A^{\prime}\right)=1-1 / 2=1 / 2$
$P\left(B^{\prime}\right)=1-1 / 3=2 / 3$
$\therefore$ Probability that neither solves (Independent events):
$P\left(A^{\prime} \cap B^{\prime}\right)=P\left(A^{\prime}\right) \times$ $P\left(B^{\prime}\right)$
$=\frac{1}{2} \times \frac{2}{3}$
$=\frac{1}{3}$
$\therefore$ Probability that the problem is solved:
$P($ Solved $)=1-P($ None solve it $)$
$P=$ $1-\frac{1}{3}$
$=\frac{2}{3}$

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