Question

there are 45 green, 13 white, 27 purple and 11 blue gumballs in the gumball machine. sharee wants to get a white or green gumball. a) what is the probability of getting a blue gumball? b) what is the probability of getting a purple gumball? c) what is the probability that she will get a blue or purple gumball? show all your work!

Explanation:

Step1: Calculate total gumballs

$45 + 13+27 + 11=96$

Step2: Calculate probability of blue gumball

The number of blue gumballs is 11. Probability formula is $P(A)=\frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}$. So $P(\text{blue})=\frac{11}{96}$

Step3: Calculate probability of purple gumball

The number of purple gumballs is 27. So $P(\text{purple})=\frac{27}{96}=\frac{9}{32}$

Step4: Calculate probability of blue or purple gumball

Use the formula $P(A\cup B)=P(A)+P(B)$ for mutually - exclusive events. $P(\text{blue or purple})=P(\text{blue})+P(\text{purple})=\frac{11}{96}+\frac{27}{96}=\frac{11 + 27}{96}=\frac{38}{96}=\frac{19}{48}$

Answer:

a) $\frac{11}{96}$
b) $\frac{9}{32}$
c) $\frac{19}{48}$