Question

chapter 1 review homework

1. there are 34 panda stickers, 24 elephant stickers, 32 smiley face stickers and 12 star stickers in the sticker machine. tara wants to get a star sticker or a panda sticker.

a) find the probability of getting a star sticker.
b) find the probability of getting a panda sticker.
c) what is the probability that she will get a star sticker or a panda sticker? show all your work!
d) find the probability of not getting a smiley face sticker.

Explanation:

Step1: Calculate total number of stickers

$34 + 24+32 + 12=102$

Step2: Calculate probability of star - sticker (a)

The probability formula is $P(A)=\frac{n(A)}{n(S)}$, where $n(A)$ is the number of favorable outcomes and $n(S)$ is the total number of outcomes. For star - stickers, $n(A) = 12$ and $n(S)=102$. So $P(\text{star})=\frac{12}{102}=\frac{2}{17}$

Step3: Calculate probability of panda - sticker (b)

For panda - stickers, $n(A) = 34$ and $n(S)=102$. So $P(\text{panda})=\frac{34}{102}=\frac{1}{3}$

Step4: Calculate probability of star or panda (c)

Since the events of getting a star sticker and a panda sticker are mutually - exclusive, $P(\text{star or panda})=P(\text{star})+P(\text{panda})$. Substitute the values: $\frac{12}{102}+\frac{34}{102}=\frac{12 + 34}{102}=\frac{46}{102}=\frac{23}{51}$

Step5: Calculate probability of not getting a smiley - face sticker (d)

The number of smiley - face stickers is 32. The probability of getting a smiley - face sticker is $P(\text{smiley})=\frac{32}{102}=\frac{16}{51}$. The probability of not getting a smiley - face sticker is $P(\text{not smiley})=1 - P(\text{smiley})=1-\frac{16}{51}=\frac{51-16}{51}=\frac{35}{51}$

Answer:

a) $\frac{2}{17}$
b) $\frac{1}{3}$
c) $\frac{23}{51}$
d) $\frac{35}{51}$