Question

1-80. tom keeps all of his favorite marbles in a special leather bag. right now, five red marbles, four blue marbles, and three yellow marbles are in the bag. homework help a. if he randomly chooses one marble to give to a friend, what is the probability that it is blue? b. tom does not really want to give away blue marbles and would like to change the probability that he chooses a blue marble to $\frac{1}{10}$. how many marbles that are not blue could he add to the bag so that the probability of choosing a blue marble becomes $\frac{1}{10}$?

Explanation:

Step1: Calculate total marbles

The total number of marbles initially is \(5 + 4+3=12\).

Step2: Calculate probability of choosing blue marble (part a)

The probability \(P\) of choosing a blue marble is the number of blue marbles divided by the total number of marbles. So \(P=\frac{4}{12}=\frac{1}{3}\).

Step3: Set up equation for part b

Let \(x\) be the number of non - blue marbles added. The number of blue marbles is still 4, and the total number of marbles becomes \(12 + x\). We want \(\frac{4}{12 + x}=\frac{1}{10}\).

Step4: Solve the equation for \(x\)

Cross - multiply: \(4\times10=12 + x\). So \(40=12 + x\). Then \(x = 40-12=28\).

Answer:

a. \(\frac{1}{3}\)
b. 28