Question

Wine quality and soil.The Journal of Wine Research(Vol.21, 2010) published a study of the effects of soil and climate on the quality of wine produced in Spain. The soil at two vineyards— Llarga and Solar—was the focus of the analysis.Wine produced from grapes grown in each of the two vineyards

was evaluated for each of three different years (growing seasons) by a wine-tasting panel. Based on the taste tests, the panel (as a group) selected the wine with the highest quality.

a.How many different wines were evaluated by the panel, where one wine was produced for each vineyard/growing season combination?

b.If the wines were all of equal quality, what is the probability that the panel selected a Llarga wine as the wine with the highest quality?

c.If the wines were all of equal quality, what is the probability that the panel selected a wine produced in year 3 as the wine with the highest quality?

d.The panel consisted of four different wine tasters who performed the evaluations independently of each other. If the wines were all of equal quality, what is the probability that all four tasters selected a Llarga wine as the wine with the highest quality?

Short answer

1. The panel evaluated the different wines in two vineyards is 6.
2. The probability that the panel selected a Llarga wine as the wine with the highest quality is 0.5.
3. The probability that the panel selected a wine produced in year 3 as the wine with the highest quality 0.3.
4. The probability that all four tasters selected a Llarga wine as the wine with the highest quality 0.063.

Step-by-step solution

Given information

A study on the impact of soil and climate on the quality of wine produced in Spain was published in The Journal of Wine Research (Vol. 21, 2010).The investigation focused on the soil at two vineyards, Llarga and Solar.The wine produced from grapes grown in each of the two vineyardswas evaluated for each of three different years (growing seasons) by a wine-tasting panel. The panel (as a whole) decided on the wine with the highest quality based on the tasting tests.

The different wines were evaluated by the panel. 

For the result apply the formula of combination.$=23=6$

So, six distinct wines from two vineyards were assessed by the panel.

Possibility that a Llarga wine was chosen by the panel as the best wine

The probability the value of combination is 6 and there are 3 panels for Llarge wine then the probability is $\frac{3}{6}=0.5$.

So, there is a 0.5 percent chance that the panel chose a Llarga wine as the best wine.

The probability that the panel selected a wine produced in year 3 as the wine with the highest quality.

The probability the value of combination is 6 in past three years and there are 2 combinationsthen the probability is $\frac{2}{6}=0.3$.

Therefore, there is a 0.3 chance that the panel would choose a wine made in year 3 as the wine with the highest quality.

The probability that all four tasters selected a Llarga wine as the wine with the highest quality

The require formula is

$\begin{array}{rcl}P\text{(four individual tasters)}& =& P{\text{(Llarge wine)}}^4\\ & =& {\text{(}0.5\text{)}}^4=0.063\\ & & \end{array}$

Hence, the likelihood that each of the four tasters picked a Llarga wine as the best wine is 0.063.