Question

the following table shows the results of a coffee taste test given at a local grocery store.

a) if one of these individuals is selected at random, find the probability that they prefer brand a coffee.
b) if one of these individuals is selected at random, find the probability that they prefer brand a coffee, given that a woman is selected.

a) the probability that they prefer brand a coffee is .
(round to four decimal places as needed.)

b) the probability that they prefer brand a coffee, given that a woman is selected, is .
(round to four decimal places as needed.)

Explanation:

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<reasoning>

Calculate probability of preferring Brand A

Using the Theoretical Probability knowledge point
\[
P(\text{Brand A}) = \frac{\text{Total preferring Brand A}}{\text{Total individuals}} = \frac{864}{2481} \approx 0.34824667
\]
Rounding to four decimal places:
\[
P(\text{Brand A}) \approx 0.3482
\]

Calculate conditional probability given a woman

Using the Conditional Probability knowledge point
\[
P(\text{Brand A} \mid \text{Woman}) = \frac{\text{Women preferring Brand A}}{\text{Total women}} = \frac{321}{980} \approx 0.32755102
\]
Rounding to four decimal places:
\[
P(\text{Brand A} \mid \text{Woman}) \approx 0.3276
\]
</reasoning>

<answer>

Question a

The probability that they prefer brand A coffee is <blank>0.3482</blank>.

Question b

The probability that they prefer Brand A coffee, given that a woman is selected, is <blank>0.3276</blank>.
</answer>

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Answer:

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<reasoning>

Calculate probability of preferring Brand A

Using the Theoretical Probability knowledge point
\[
P(\text{Brand A}) = \frac{\text{Total preferring Brand A}}{\text{Total individuals}} = \frac{864}{2481} \approx 0.34824667
\]
Rounding to four decimal places:
\[
P(\text{Brand A}) \approx 0.3482
\]

Calculate conditional probability given a woman

Using the Conditional Probability knowledge point
\[
P(\text{Brand A} \mid \text{Woman}) = \frac{\text{Women preferring Brand A}}{\text{Total women}} = \frac{321}{980} \approx 0.32755102
\]
Rounding to four decimal places:
\[
P(\text{Brand A} \mid \text{Woman}) \approx 0.3276
\]
</reasoning>

<answer>

Question a

The probability that they prefer brand A coffee is <blank>0.3482</blank>.

Question b

The probability that they prefer Brand A coffee, given that a woman is selected, is <blank>0.3276</blank>.
</answer>

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