Question

1) A grocery store carries the following items. There are two main categories of food – conventional and organic ingredients – and four food groups. The data are shown in the following table. Food Groups Food Categories Grains Fruits Vegetables Meat Total Conventional 82 48 276 204 610 Organic 93 77 24 11 205 Total 175 125 300 215 815 If all of the grains and meats were accidentally displayed together without a sticker or label to mark their origin, what is the probability that you select a grain or meat that is conventional into your grocery basket? First compute for yourself the row (i.e., n1+, n2+), column (i.e., n+1, n+2, n+3, n+4), and overall (i.e., n++) totals, to aid in answering the question. Answer:

2) Suppose at random 39% of school children develop nausea and vomiting following holiday parties and that you conduct a study to examine this phenomenon, with a sample size of n=12. What is the probability that between more than 6 and 10 or less children become sick?

3)

A grocery store carries the following items. There are two main categories of food – conventional and organic ingredients – and four food groups. The data are shown in the following table.

	Food Groups
Food Categories	Grains	Fruits	Vegetables	Meat	Total
Conventional	90	5	10	111	216
Organic	85	120	290	104	599
Total	175	125	300	215	815

If all of the items were accidentally displayed together without a sticker or label to mark their origin, what is the probability that you select an organic grain, vegetable, or meat in your grocery basket? First compute for yourself the row (i.e., n₁₊, n₂₊), column (i.e., n₊₁, n₊₂, n₊₃, n₊₄), and overall (i.e., n₊₊) totals, to aid in answering the question.

Answer:

Answer 1

1) A grocery store carries the following items. There are two main categories of food – conventional and organic ingredients – and four food groups. The data are shown in the following table. Food Groups Food Categories Grains Fruits Vegetables Meat Total Conventional 82 48 276 204 610 Organic 93 77 24 11 205 Total 175 125 300 215 815 If all of the grains and meats were accidentally displayed together without a sticker or label to mark their origin, what is the probability that you select a grain or meat that is conventional into your grocery basket? First compute for yourself the row (i.e., n1+, n2+), column (i.e., n+1, n+2, n+3, n+4), and overall (i.e., n++) totals, to aid in answering the question.

	Food Groups
Food Categories	Grains	Fruits	Vegetables	Meat	Total
Conventional	82	48	276	204	610
Organic	93	77	24	11	205
Total	175	125	300	215	815

Probability that selected conventional item is grain or meat = P( Grain | Conventional ) + P(Meat | Conventional)

We add their probability since question ask 'or'. We rule out the probability of them being both.

P( Grain | Conventional ) is the proportion of grain out of the total conventional and P(Meat | Conventional ) is the proportion of meat out of the total conventional.

Probability that selected conventional item is grain or meat =

= 0.4689

Answer:

2) Suppose at random 39% of school children develop nausea and vomiting following holiday parties and that you conduct a study to examine this phenomenon, with a sample size of n=12. What is the probability that between more than 6 and 10 or less children become sick?

This is an example of binomial distribution where 'X' is the no. of children developing sickness.

.............Since 39% = 0.39

P (X = x) = ..............where q = 1 - p = 0.61

This is a discrete distribution so can't be same.

Probability that between more than 6 and 10 or less children become sick is

= P ( X = 7) + P (X = 8) + P( X = 9) + P( X = 10)

= + ...........+

= 0.0918 + 0.3668 + 0.01042 + 0.002

= 0.1409

Answer:

3) A grocery store carries the following items. There are two main categories of food – conventional and organic ingredients – and four food groups. The data are shown in the following table.

	Food Groups
Food Categories	Grains	Fruits	Vegetables	Meat	Total
Conventional	90	5	10	111	216
Organic	85	120	290	104	599
Total	175	125	300	215	815

If all of the items were accidentally displayed together without a sticker or label to mark their origin, what is the probability that you select an organic grain, vegetable, or meat in your grocery basket? First compute for yourself the row (i.e., n₁₊, n₂₊), column (i.e., n₊₁, n₊₂, n₊₃, n₊₄), and overall (i.e., n₊₊) totals, to aid in answering the question.

Out of the total items we want to know the probability of selecting organic grain , meat or vegetable .

P ( Organic grain) + P( organic meat) + P(Organic Vegetable) =

= 0.5877

Answer;

In the first question the words are framed in the way that 'we know selected item is conventional but we don't what food group'. Hence we calculated proportion out of conventional.

But in 3rd, we didn't know beforehand which food category the selected item belonged to. They asked for the proportion of organic food groups out of total food items.