Your backpack contains a fruit left from Sunday, that\'s either an apple or an o

Question

Your backpack contains a fruit left from Sunday, that's either an apple or
an orange with equal probability. On Monday morning, before coming to school, you put
an orange in your backpack (without looking inside).

1) After class you get hungry, so you reach inside and grab a fruit at random, that turns
out to be an orange. What's the probability that the remaining fruit is also an orange?
2) On Tuesday morning, before coming to school, you put an apple in your backpack
(without looking inside). After class, you get hungry, so you reach inside and grab
a fruit at random, that turns out to be an apple. What's the probability that the
remaining fruit is also an apple?

Explanation / Answer

1 On Sunday, one is left with either an orange or an apple, and on Monday an apple is inserted. The sample space consists of outcomes, S:{AO, OO}. Therefore, the probability that remaining fruit is also orange, is P(OO)=1/2=0.5

2. On Monday, one is left with either an orange or an apple. On tuesday, an apple is inserted. The sample space consists of outcomes, S:{OA, AA}. The probability that the remaining fruit is also an apple, is P(AA)=1/2= 0.5

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