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# probability and statistics

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The eyesight of 7477 women aged 30 to 39 who were employed in Royal Ordnance factories was assessed. Each eye was graded separately on a scale from 1 (very good) to 4 (poor). The results are shown in the table below.

 left eye grade total 1 2 3 4 right 1 1520 266 124 66 1976 eye 2 234 1512 432 78 2256 grade 3 117 362 1772 205 2456 4 36 82 179 492 789 total 1907 2222 2507 841 7477

One woman is selected at random from these 7477 women.

What is the probability that this woman has grade 1 or 2 eyesight in both eyes?

What is the probability that this woman does not have grade 4 eyesight in her left eye?

Jun 11, 2020
edited by Guest  Jun 11, 2020

### 1+0 Answers

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The table is nearly impossible to read; also, I can't find a way for the numbers in the first row to sum to 1976.

Anyway:

What is the probability that a woman, selected at random, has grade 1 or 2 eyesight in both eyes?

--  Add up four numbers:

the number with grade 1 in left eye and grade 1 in right eye;

the number with grade 1 in left eye and grade 2 in right eye;

the number with grade 2 in left eye and grade 1 in right eye;

the number with grade 2 in left eye and grade 2 in right eye;

and divide this total by the total number of women.

What is the probability that this woman does not have grade 4 eyesight in her left eye?

--  Find the entry for grade 4 eyesight in her left eye; subtract this from the total number of women;

divide this answer by the total number of women.

Jun 11, 2020