Suppose that Jennifer has a 90% probability to eat breakfast and David has a 30%

Question

Suppose that Jennifer has a 90% probability to eat breakfast and David has a 30% proba- bility to eat breakfast. Moreover, assume whether Jennifer eats breakfast is not related to whether David eats breakfast.

(a) What’s the probability that both Jennifer and David eat breakfast tomorrow morning?

(b) What’s the probability that Jennifer eats breakfast or David eats breakfast tomorrow morning?

(c) What’s the probability that either Jennifer or David (not both of them) eats breakfast tomorrow morning?

Explanation / Answer

P(Jennifer) = 0.90 , P(David) = 0.30

a)

Since whether Jenifer eats breakfast is not related to whether David eats breakfast, both events

are independent.

Therefore,

P(Both Jenifer and David eats breakfast) = P(Jenifer eats breakfast) * P(David eats breakfast)

= 0.90 * 0.30

= 0.27

b)

P(Jenifer or David eats breakfast) = P(Jenifer) + P(David) - P(Jenifer and David)

= 0.90 + 0.30 - 0.27

= 0.93

c)

P(either Jenifer or David) = P(Jenifer)* P(not David) + P(David) * P(not Jenifer)

= 0.90 * ( 1 - 0.30) + .30 * (1 - 0.90)

= 0.90 * 0.70 + 0.30 * 0.10

= 0.66

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