Question

question 4
this venn diagram shows sports played by 10 students.

let event a = the student plays basketball.
let event b = the student plays soccer.
what is $p(a \text{ or } b)$?
a. $\frac{7}{10}$
b. $\frac{3}{10}$
c. $\frac{1}{2}$
d. $\frac{1}{5}$

question 5
angel and isaiah have forgotten whose turn it is to mow the lawn. how can they make a fair decision?
select all the correct answers.
a. put each persons name on a separate piece of paper in a bag. randomly draw a name. the person whose name is chosen mows the lawn.
b. roll a number cube. if the number rolled is 1 or 6, angel mows the lawn. if it is any other number, isaiah mows the lawn.
c. flip a coin. if it comes up heads, angel mows the lawn. if it comes up tails, isaiah mows the lawn.
d. flip a coin twice. if either toss is tails, angel mows the lawn. otherwise, isaiah mows the lawn.

Explanation:

Question 4

Step1: Count total students

Total students = 10

Step2: Count students in A or B

Students in A (basketball): Fran, Juan, Ian, Ella (4)
Students in B only (soccer): Mickey, Mei, Marcus (3)
Total for A or B = 4 + 3 = 7

Step3: Calculate probability

$P(A \text{ or } B) = \frac{\text{Number of students in A or B}}{\text{Total students}}$
$P(A \text{ or } B) = \frac{7}{10}$

• Option A: Each name has an equal $\frac{1}{2}$ chance of being drawn, so it is fair.
• Option B: Angel has a $\frac{2}{6}=\frac{1}{3}$ chance, Isaiah has a $\frac{4}{6}=\frac{2}{3}$ chance; unequal probabilities, so unfair.
• Option C: A fair coin has a $\frac{1}{2}$ chance for heads and tails, so each person has an equal chance, making it fair.
• Option D: The only outcome Isaiah mows is two heads ($\frac{1}{4}$ chance), Angel mows in 3 out of 4 outcomes ($\frac{3}{4}$ chance); unequal probabilities, so unfair.

Answer:

A. $\frac{7}{10}$

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Question 5