Question

columns represent the different types of fruit for sale.
use the frequency table to compute the following.
probability of buying a pint of apricots:
p(a) =
probability of buying a pint of cherries:
p(b) =
probability of buying a pint of apricots and buying a
pint of cherries:
p(a and b) =

Explanation:

Step1: Calculate \( P(A) \)

The formula for probability is \( P = \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}} \).
For \( P(A) \) (probability of buying apricots), the number of apricots is \( 133 \) and the total number of fruits is \( 401 \). So \( P(A)=\frac{133}{401}\approx0.332 \)

Step2: Calculate \( P(B) \)

For \( P(B) \) (probability of buying cherries), the number of cherries is \( 128 \) and the total number of fruits is \( 401 \). So \( P(B)=\frac{128}{401}\approx0.319 \)

Step3: Calculate \( P(A\cap B) \)

Since buying a pint of apricots and a pint of cherries are two - separate non - simultaneous events (assuming a single purchase), and using the formula \( P(A\cap B)=P(A)\times P(B) \) (if events are independent).
\( P(A\cap B)=\frac{133\times128}{401\times401}=\frac{17024}{160801}\approx0.106 \)

Answer:

\( P(A)=\frac{133}{401}\approx0.332 \), \( P(B)=\frac{128}{401}\approx0.319 \), \( P(A\cap B)=\frac{133\times128}{401\times401}\approx0.106 \)