Question

5 formula 2 points
a gumball machine contains 12 red gumballs and 3 white gumballs. two gumballs are purchased, one after the other, without replacement. find the probability that at least one gumball is white.
express your answer as a decimal, rounded to the nearest hundredth.
answer
0.37

Explanation:

Step1: Calculate the total number of gumballs

The total number of gumballs is \(12 + 3=15\).

Step2: Calculate the probability that no gumball is white

The probability that the first gumball is not white is \(\frac{12}{15}\). After taking out a non - white gumball, the number of non - white gumballs is \(11\) and the total number of gumballs is \(14\). So the probability that the second gumball is also not white is \(\frac{11}{14}\). Then the probability that no gumball is white is \(\frac{12}{15}\times\frac{11}{14}=\frac{132}{210}=\frac{22}{35}\approx0.63\).

Step3: Calculate the probability that at least one gumball is white

Use the formula \(P(\text{at least one white}) = 1 - P(\text{no white})\). So \(P = 1-\frac{22}{35}=\frac{35 - 22}{35}=\frac{13}{35}\approx0.37\).

Answer:

\(0.37\)