16. A group of freshmen at a local university consider joining the equestrian te

Question

16. A group of freshmen at a local university consider joining the equestrian team. Students choose Westem riding with probability P 35, dressage with probability P 0.45, and jumping with probability P 0.40. The probability that a student chooses both dressage and jumping is P 0.15, while the probability of a student choosing Western and dressage is P- 0.10. No one chooses Western and jumping. There are no horses suitable for both and each student is assigned to one horse. What is the probability that a student chooses neither dressage nor Western riding?

Explanation / Answer

P( dressage) = 0.45, P(Western riding) = 0.35 , P(dressage AND Western riding) = 0.10

Therefore,

P(dressage OR Western riding) = P( dressage) + P(Western riding)

- P(dressage AND Western riding)

= 0.35 + 0.35 - 0.10

= 0.60

So,

P(Neither dressage nor Western riding) = 1 - P(dressage OR Western riding)

= 1 - 0.65

= 0.35

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