Problem

A marble jar contains a total of 164 marbles. The frequency of each color marble is listed in the chart below. \begin{tabular}{|l|l|l|l|l|l|l|} \hline Color & Red & Blue & Green & White & Yellow & Orange \\ \hline Frequency & 37 & 34 & 17 & 26 & 21 & 29 \\ \hline \end{tabular} Suppose that two marbles will be randomly selected from the jar without replacement. Determine the probability that a Yellow marble is chosen followed by a White one. Round as indicated on the formula sheet.

Solution

Step 1 :The problem involves a jar of 164 marbles with different colors. The frequency of each color is as follows: Red - 37, Blue - 34, Green - 17, White - 26, Yellow - 21, Orange - 29.

Step 2 :We are asked to find the probability of drawing a Yellow marble first and then a White marble, without replacement.

Step 3 :The probability of an event is calculated by dividing the number of ways the event can occur by the total number of outcomes.

Step 4 :The number of ways a Yellow marble can be chosen first is the number of Yellow marbles in the jar, which is 21. After a Yellow marble is chosen, it is not replaced, so the total number of marbles in the jar decreases by 1, to 163.

Step 5 :The number of ways a White marble can be chosen next is the number of White marbles in the jar, which is 26.

Step 6 :The total number of ways two marbles can be chosen from the jar is the number of ways to choose 2 marbles from 164, which is the combination of 164 taken 2 at a time, denoted as \(C(164, 2)\).

Step 7 :So, the probability that a Yellow marble is chosen followed by a White one is \((21/164) * (26/163)\).

Step 8 :Calculating the above expression, we get the probability as 0.0204.

Step 9 :Final Answer: The probability that a Yellow marble is chosen followed by a White one is \(\boxed{0.0204}\).

From Solvely APP
Source: https://solvelyapp.com/problems/8286/

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