there are 45 green, 13 white, 27 purple and 11 blue gumballs in the gumball machine. sharee wants to get a…
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!
Answer
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) $\frac{19}{48}$