---
title: Practice Test Answers_Probability
tags: Practice, Test, Probability
description: Answers and highlight for practice test
type: pdf
slideOptions:
theme: white

---

### **Part A Number in Math**

<br/>
<br/>

1.

a. $\frac{1}{2}$;
b. $\frac{1}{4}$;
c. $\frac{3}{4}$

<div class="alert alert-info">For c, remember this is the complementary of probability, we use 1 - pr(Event) to get the probability of NOT Event</div>

<br/>

2.

a. $\frac{2}{5}$
b. $(\frac{2}{5})^2 = \frac{4}{25}$
c. $5\times 3 \times \frac{3}{5} = 9$
<div class="alert alert-info">For b, think about how we do in in a probability tree</div>

<br/>

3.

a. 5th row: $6,7,8,9,10,11$; 6th row: $7,8,9,10,11,12$
b. $\frac{4}{36}=\frac{1}{9}$
c. $\frac{30}{36} = \frac{5}{6}$, or $1-\frac{6}{36} = 1-\frac{1}{6}=\frac{5}{6}$
d. We have two 3s, five 6s, four 9s, and one 12. So 2 + 5 + 4 + 1 = 12, then the answer is $\frac{12}{36} = \frac{1}{3}$
e. there are 11 cases that One of the dice roll a "1"; there are 10 cases that the sum is greater than 8, so $\frac{10}{36} < \frac{11}{36}$. It is more likely for One of the dice roll a "1".

4.

$\frac{12}{52} = \frac{3}{13}$

<br/>

5.

a.
- Initial branch: Face: $\frac{12}{52}$ = $\frac{3}{13}$; Non-Face: $\frac{40}{52}=\frac{10}{13}$
- Face Card branch: Face: $\frac{11}{51}$; Non-Face: $\frac{40}{51}$
- Non-Face Card branch: Face: $\frac{12}{51}=\frac{4}{17}$; Non-Face: $\frac{39}{51}=\frac{13}{17}$
- P(2 face Cards) = $\frac{12}{52}\times \frac{11}{51} = \frac{11}{221}$

b. $\frac{12}{52} \times \frac{40}{51} + \frac{40}{52}\times\frac{12}{51}= 2 \times \frac{12\times 40}{52\times 51} = \frac{80}{221}$

<div class="alert alert-info">This is tricky one. So you need to consider whether the denominator has decreased.</div>

<br/>

### **Part B**

<br/>
<br/>

Question one: Snacks

a. B. $25$
b. $\frac{8}{25}$
c. $\frac{8}{25} \times \frac{4}{24} = \frac{32}{600} = \frac{4}{75}$
<div class="alert alert-info">For c, similar logic like the previous question. Two students are drawning, for the second one, sample space changed.</div>

<br/>

Question Two: Mammals

a. B. $\frac{3}{25}$
b. $\frac{7}{25}$
c. $\frac{9}{25} = 36\%$

<br/>
<br/>

Question Three: Basketball

a. C. $50$
b. $\frac{28}{50} = \frac{14}{25}$
c. $\frac{12}{50} = \frac{6}{25}$
d. $\frac{12}{27} = \frac{4}{9}$
e. Comparing $\frac{12}{27}$ and $\frac{10}{23}$, which one is bigger?

<br/>
<br/>

Question Four:

a. $\frac{1}{4}$
b. $\frac{15}{16}$
c. No. $\frac{9}{20}\times \frac{11}{20} \times 2 = \frac{198}{400} = \frac{99}{200}$, whick is less than half.

<br/>
<br/>

### **Part End**