ดูต้นฉบับสำหรับ Probstat/week2 practice 1 solutions

This are solutions to [[Probstat/week2 practice 1]].

== Conditional probability review ==

1.1 There are 7 numbers divisible by 2 and 3 (0, 6, 12, 18, 24, 30, 36).  There are 14 numbers divisible by 3.  Let '''A''' be the event that a random number is divisible by 3.  Let '''B''' be the event that a random number is divisible by 2.  We want to compute '''P(B|A)''', which is '''P(AB)/P(A)''' = 7/14 = 1/2.

1.2 Using the definition of events '''A'''and '''B''' from question 1.1, note that '''P(B) = 21/42 = 1/2'''.  Thus '''P(B|A) = P(B)'''.  This implies that '''P(AB)=P(A)P(B)'''.  Therefore, both events are independent.

1.3 The number divisible by 4 and 3 are 0, 12, 24, and 36.  Let '''C''' be the event that a random number is divisible by 4.  Thus, '''P(C|A)''' = 4/14 = 1/7.

1.4 Note that '''P(C)''' = 11/42.  This is not equal to '''P(C|A)'''.  Therefore both events are not independent.