Pollution of the rivers in the united states has been a problem for many years. consider the following events: a: the river is polluted, b: a sample of water tested detects pollution, c : fishing is permitted. assume p(a) = 0.3, p(b|a) = 0.75, p(b|ac ) = 0.2, p c|a∩b = 0.2, p c|ac∩b = 0.15, p c|a∩bc = 0.8 and p c|ac ∩ bc = 0.9, then find (1) p(a ∩ b ∩ c) (2) p(bc ∩ c) (3) p(c) (4) find the probability that the river is polluted, given that fishing is permitted and the sample tested did not detect pollution. hint: de-morgan’s law (a ∩ b) c = ac ∪ b

(1) 0.045 (2) 0.564 (3) 0.63 (4) 0.1064

Step-by-step explanation:

We use the multiplication rule several times

(1) = (0.2)(0.75)(0.3) = 0.045

(2) =

(0.8)(0.25)(0.3) + (0.9)(0.8)(0.7) =  0.564

(3) =

0.045 + = 0.045 + (0.15)(0.2)(0.7) = 0.066

= 0.066 + 0.564 = 0.63

(4)

= (0.8)(0.25)(0.3)/0.564 = 0.1064

8 apples are left.

step-by-step explanation:

10-2=8

10 apples

take 2

now u have 8

the terms of a geometric sequence can be found by beginning with the first term and multiplying by the common ratio repeatedly. a recursive formula for a geometric sequence with common ratio r is given by an=ran−1 a n = r a n − 1 for n≥2 n ≥ 2 .

step-by-step explanation: