Given that P(B|A)=0.86 and P(A)=0.43, what is P(B AND A)? Round to three decimal places.

Step-by-step explanation:

P(B|A)=[P(A and B)]/[P(A)]

0.86=[P(A and B)]/0.43

P(A and B)=0.86×0.43=0.3698≈0.340

Part (a)

Let's replace x with 15 and evaluate to see if he is correct or not.

x/2 - 3 = 6

15/2 - 3 = 6

7.5 - 3 = 6  

4.5 = 6

We get a false statement after simplifying everything. We need to get the same number on both sides to get a true statement. Therefore, Ahmed is not correct.

Part (b)

Let's solve for x. We do so by first adding 3 to both sides, and then multiplying both sides by 2. This follows PEMDAS in reverse, undoing everything to isolate the variable.

x/2 - 3 = 6

x/2 = 6+3 add 3 to both sides

x/2 = 9

x = 9*2 multiply both sides by 2

x = 18 is the answer

As a check, we'll use the same idea as part (a)

x/2 - 3 = 6

18/2 - 3 = 6

9 - 3 = 6

6 = 6

We get a true statement this time. This confirms x = 18