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.
