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 ∩ _ a3)
___________
P ( _a4)

Question

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Respuesta :

tramserran tramserran · Answer 1 · 2020-06-11T12:12:10+02:00

Answer: [tex]\bold{P(B|A)=\dfrac{P(B\cap A)}{P(A)}=\dfrac{11}{30}}[/tex]

Step-by-step explanation:

The probability of Event B given Event A = the intersection of Event A and B divided by the probability of Event A. (see below for the symbols)

[tex]P(B|A)=\dfrac{P(B\cap A)}{P(A)}[/tex]

P(A) = (1, 6), (1, 5), (1, 4), (1, 3), (1, 2), (1, 1)

(2, 6), (2, 5), (2, 4), (2, 3), (2, 2), (2, 1)

(3, 6), (3, 5), (3, 4), (3, 3), (3, 2), (3, 1)

(4, 5), (4, 4), (4, 3), (4, 2), (4, 1)

(5, 4), (5, 3), (5, 2), (5, 1)

(6, 3), (6, 2), (6, 1)

= 30

P(B) = (1, 2), (2, 1) sum = 3

(1, 5), (2, 4), (3, 3), (4, 2), (5, 1) sum = 6

(3, 6), (4, 5), (5, 4), (5, 4), (6, 3) sum = 9

(6, 6) sum = 12

= 12

P(A ∩ B) = (1, 2), (2, 1)

(1, 5), (2, 4), (3, 3), (4, 2), (5, 1)

(3, 6), (4, 5), (5, 4), (5, 4), (6, 3)

= 11