Question

2-28 lila is making a spinner game for her cousins to play. she divided it into 8 equal sections and has labeled each section with a symbol. when the spinner lands on a flower (🌸), her cousin will win a prize.
a) what is p(⭐)? express your answer as a fraction, as a decimal, and as a percent.
b) what is the probability of not getting ⬛? write your answer as a fraction, as a decimal, and as a percent.
c) what is p(🌸)? express your answer as a fraction, as a decimal, and as a percent.
d) if lila’s cousins spin 100 times, about how many times would you expect them to spin a heart (❤️)?

Explanation:

Step1: Recall probability formula

Probability $P(E)=\frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}$. The spinner has 8 equal - sections, so the total number of outcomes is 8.

Step2: Solve part a

There are 3 star - sections. So $P(\star)=\frac{3}{8}=0.375 = 37.5\%$.

Step3: Solve part b

There is 1 diamond - section. The probability of getting a diamond is $P(\diamond)=\frac{1}{8}$. The probability of not getting a diamond is $P(\text{not }\diamond)=1 - P(\diamond)=1-\frac{1}{8}=\frac{7}{8}=0.875 = 87.5\%$.

Step4: Solve part c

There are 2 flower - sections. So $P(\text{flower})=\frac{2}{8}=\frac{1}{4}=0.25 = 25\%$.

Step5: Solve part d

There are 2 heart - sections. The probability of spinning a heart is $P(\text{heart})=\frac{2}{8}=\frac{1}{4}$. If the spinner is spun 100 times, the expected number of times to spin a heart is $n = P(\text{heart})\times\text{Number of spins}=\frac{1}{4}\times100 = 25$ times.

Answer:

a) $\frac{3}{8}$, $0.375$, $37.5\%$
b) $\frac{7}{8}$, $0.875$, $87.5\%$
c) $\frac{1}{4}$, $0.25$, $25\%$
d) 25 times