Eighty-five percent of UCD students are Irish. Forty percent of UCD students play rugby. Thirty five...

Eighty-five percent of UCD students are Irish. Forty percent of UCD students play rugby. Thirty five percent of students are Irish and play rugby. If a student is selected at random, find the conditional probability that:

(a) the student practices rugby, given that the he/she is Irish;

(b) the student is Irish, given that the he/she practices rugby. List all the properties/theorems you have used in your calculations.

Expert Solution

P(Irish) = 0.85

P(play rugby) = 0.4

P(Irish and play rugby) = 0.35

a) P(play rugby | Irish) = P(Irish and play rugby) / P(Irish)

= 0.35 / 0.85

= 0.4118

b) P(Irish | play rugby) = P(Irish and play rugby) / P(play rugby)

= 0.35 / 0.4

= 0.875

orchestra answered 1 year ago

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