Question

a box contains 24 fruit bars. the probability of choosing a cherry, apple, or strawberry bar is \\( \frac{3}{4} \\). the probability of choosing a cherry bar is \\( \frac{1}{6} \\). the probability of choosing an apple bar equals the probability of choosing a strawberry bar. how many strawberry bars are in the box? strawberry bars

Explanation:

Step1: Define variables for probabilities

Let $P(C)$ = probability of cherry bar, $P(A)$ = probability of apple bar, $P(S)$ = probability of strawberry bar.
Given $P(C) + P(A) + P(S) = 1$, $P(C)=\frac{1}{2}$, and $P(A)=P(S)$.

Step2: Substitute known probability

Substitute $P(C)=\frac{1}{2}$ into the total probability equation:
$\frac{1}{2} + P(A) + P(S) = 1$

Step3: Use equal probability condition

Since $P(A)=P(S)$, replace $P(A)$ with $P(S)$:
$\frac{1}{2} + 2P(S) = 1$

Step4: Solve for $P(S)$

Subtract $\frac{1}{2}$ from both sides:
$2P(S) = 1 - \frac{1}{2} = \frac{1}{2}$
Divide by 2:
$P(S) = \frac{1}{4}$

Step5: Calculate number of strawberry bars

Total bars = 20. Number of strawberry bars = $20 \times P(S)$
$20 \times \frac{1}{4} = 5$

Answer:

5 strawberry bars