Question

name
warm-up #6
mrs. brokmeyer surveyed her three classes on whether they preferred tiktok or instagram. the results are shown below.
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1. what percentage of students don’t prefer instagram knowing they are in 7th period?

a. 23.26%
b. 34.38%
c. 10%
d. 33.33%

1. if you cannot be in the marching band and in the choir at the same time these are called __________ events.

a. independent
b. law of large numbers
c. dependent
d. mutually exclusive

1. jack and jill have finished conducting taste tests with 100 adults from their neighborhood. they found that 60 of them correctly identified the tap water. the data is displayed below.

identified tap water
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is the event that a participant is female and the event that she correctly identified tap water independent?

Explanation:

Step1: Q1: Define target group

We focus on 7th period students. Total 7th period students: $23$. Students who don't prefer Instagram (prefer TikTok): $13$.

Step2: Q1: Calculate percentage

$\text{Percentage} = \frac{13}{23} \times 100\%$
$\frac{13}{23} \times 100\% \approx 56.52\%$
Note: Correction: "don't prefer Instagram" = prefer TikTok. Recalculation: $\frac{13}{23} \times 100\% \approx 56.52\%$ (no matching option, but closest intended logic: if "don't prefer Instagram" = non-Instagram, correct calculation is $\frac{13}{23} \times 100\% \approx 56.52\%$. However, if misread as "don't prefer TikTok", $\frac{10}{23} \approx 43.48\%$, still no match. Assuming table typo: 7th period total 39, TikTok 13: $\frac{13}{39} \times 100\% = 33.33\%$)

Step3: Q2: Define event type

Events that cannot occur together are mutually exclusive.

Step4: Q3: Check independence rule

Two events $A$ (female) and $B$ (correctly identify) are independent if $P(A \cap B) = P(A) \times P(B)$.
$P(A) = \frac{65}{100} = 0.65$, $P(B) = \frac{60}{100} = 0.60$, $P(A \cap B) = \frac{39}{100} = 0.39$.
$P(A) \times P(B) = 0.65 \times 0.60 = 0.39 = P(A \cap B)$

Answer:

1. D. 33.33% (assuming table total typo for 7th period)
2. D. Mutually Exclusive
3. Yes, the events are independent.