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Two number cubes are rolled for two separate events:

Event A is the event that the sum of numbers on both cubes is less than 10.
Event B is the event that the sum of numbers on both cubes is a multiple of 3.

Complete the conditional-probability formula for event B given that event A occurs first by writing A and B in the blanks:

P(                                          a0 |​                                                          a1) = 

P(                                          a2 U                                               a3)

–––––––––––––––––––––––––––––––––––––––––––––––––––––

                         P(                                               a4)

 Jan 30, 2019
 #1
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\(\text{well.. the main formula they are after is}\\ P[A|B] = \dfrac{P[B|A]P[A]}{P[B]}\)

 

\(\text{here}\\ P[B|A] = P[3\cup 6 \cup 9]\\ P[A] = P[3\cup6\cup 9\cup 12]\\ P[B] = P[2-9]\)

 

\(\text{with some simple counting }\\ P[3 \cup 6 \cup 9] = \dfrac{2+5+2}{36} = \dfrac{11}{36}\\ P[3\cup 6 \cup 9 \cup 12] = \dfrac{12}{36}=\dfrac 1 3\\ P[2-9]=\dfrac{1+2+3+4+5+6+5+4}{36} = \dfrac{30}{36}=\dfrac{5}{6}\)

 

\(\dfrac{P[B|A]P[A]}{P[B]} = \dfrac{\dfrac{11}{36}\dfrac{1}{3}}{\dfrac{5}{6}}=\dfrac{11}{90}\)

.
 Jan 31, 2019

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