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Probability (p-2) — Maths (commerce) STD 11 Commerce / Arts — Question

Maharashtra BoardEnglish MediumSTD 11 Commerce / ArtsMaths (commerce)Probability (p-2)2 Marks
Question
A computer software company is bidding for computer programs A and B. The probability that the company will get software $A$ is $\frac{3}{5}$, the probability that the company will get software $B$ is $\frac{1}{3}$ and the probability that company will get both $A$ and $B$ is $\frac{1}{8}$. What is the probability that the company will get at least one software?
✓

Answer

Let $\mathrm{A}$ be the event that the company will get software $\mathrm{A}$.
$
\therefore P(A)=\frac{3}{5}
$
Let $B$ be the event that company will get software $B$.
$
\therefore P(B)=\frac{1}{3}
$
Also, $P(A \cap B)=\frac{1}{8}$
$
\begin{aligned}
& \therefore P(\text { the company will get at least one software })=P(A \cup B) \\
& =P(A)+P(B)-P(A \cap B) \\
& =\frac{3}{5}+\frac{1}{3}-\frac{1}{8} \\
& =\frac{72+40-15}{120} \\
& =\frac{97}{120}
\end{aligned}
$

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