I really need help with this... the whole thing

First, "complete" the table by counting up the totals in each category.

Total number of students that can swim:

215 + 269 + 293 = 777

Total number of students that cannot swim:

85 + 31 + 7 = 123

Total number of Year 4 students:

215 + 85 = 300

Total number of Year 7 students:

269 + 31 = 300

Total number of Year 10 students:

293 + 7 = 300

Total number of students:

777 + 123 = 300 + 300 + 300 = 900

Then the probability that a randomly selected student fall in a given category is equal to (the number of students in that category) divided by (the total number of students at the school).

(a) can swim:

777/900 = 259/300 ≈ 0.86

(b) cannot swim:

123/900 = 41/300 ≈ 0.14

(notice that this is also equal to 1 minus the probability that a student can swim)

(c) from year 7:

300/900 = 1/3 ≈ 0.33

(d) from year 7 AND cannot swim:

31/900 ≈ 0.034

(e) from year 7 OR cannot swim:

(300 + 123 - 31)/900 = 98/225 ≈ 0.44

This follows from the inclusion/exclusion principle.

P(A or B) = P(A) + P(B) - P(A and B)

(f) cannot swim, given from year 7 OR year 10:

(38/900) / (600/900) = 38/600 = 19/300 ≈ 0.063

By definition of conditional probability,

P(cannot swim | year 7 OR year 10) = P(cannot swim AND (year 7 OR year 10)) / P(year 7 OR year 10)

There are 600 students in either year 7 or 10, and according to the table, 31 + 7 = 38 of them cannot swim.

(g) from year 4, given that they cannot swim:

(85/900) / (123/900) = 85/123 ≈ 0.69

Again, by definition,

P(year 4 | cannot swim) = P(year 4 AND cannot swim) / P(cannot swim)

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step-by-step explanation: