Melina stocks her fruit stand with organic and non-organic fruits and keeps track of what is sold. The results are shown in the following probability distribution table.

\begin{tabular}{|c|c|c|c|}
\hline
& Apples & Oranges & Total \\
\hline
Organic & 0.57 & 0.13 & 0.70 \\
\hline
Non-organic & 0.19 & 0.11 & 0.30 \\
\hline
Total & 0.76 & 0.24 & 1.00 \\
\hline
\end{tabular}

What is the probability that a randomly selected orange is organic?

A. 0.75
B. 0.25
C. 0.63
D. 0.37



Answer :

To find the probability that a randomly selected orange is organic, we need to make use of conditional probability. The conditional probability [tex]\( P(\text{Organic | Orange}) \)[/tex] is calculated using the formula:

[tex]\[ P(\text{Organic | Orange}) = \frac{P(\text{Organic and Orange})}{P(\text{Orange})} \][/tex]

From the probability distribution table, we are given:

- [tex]\( P(\text{Organic and Orange}) = 0.13 \)[/tex]
- [tex]\( P(\text{Orange}) = 0.24 \)[/tex]

We can now substitute these values into the formula:

[tex]\[ P(\text{Organic | Orange}) = \frac{0.13}{0.24} \][/tex]

Performing the division:

[tex]\[ P(\text{Organic | Orange}) \approx 0.5417 \][/tex]

Therefore, the probability that a randomly selected orange is organic is approximately [tex]\( 0.5417 \)[/tex]. This is closest to the numerical value 0.54.

Given the options provided, we notice that none are exactly [tex]\( 0.54 \)[/tex]. Therefore, this detailed calculation demonstrates that the initial options may have a rounding or data entry discrepancy.

However, considering the value [tex]\( 0.5417 \)[/tex], none of the provided options:
- 0.75
- 0.25
- 0.63
- 0.37

exactly matches this probability.

So, if sticking to the closest match, [tex]\( 0.63 \)[/tex] might be the closest answer presented, but it doesn’t represent our actual calculated probability accurately.