We have:
Event A ⇒ P(A) = 0.16
Event B ⇒ P(B) = 0.09
Probability of event B given event A happening, P(B|A) = P(A∩B) / P(A) = 0.12
By the conditional probability, the probability of event A and event B happens together is given by:
P(B|A) = P(A∩B) ÷ P(A)
P(B|A) = P(A∩B) ÷ 0.16
0.12 = P(A∩B) ÷ 0.16
P(A∩B) = 0.12 × 0.16
P(A∩B) = 0.0192
When two events are independent, P(A) × P(B) = P(A∩B) so if P(A∩B) = 0.0192, then P(B) will be 0.0192 ÷ 0.16 = 0.12 (which take us back to P(B|A))
Since P(B|A) does not equal to P(B), event A and event B are not independent.
Answer: <span>Events A and B are not independent because P(B|A) ≠ P(B)</span>
Hello there! I can help you! The formula for compound interest is P(1 + r)^t, where P= principal (initial amount), r = interest rate (in decimal form), and t = time (in years). Let's do this step by step. First off, we add the rate into 1. 4% is the interest rate (0.04 in decimal form). 1 + 0.04 is 1.04. Now, what we will do is raise that number to the 2nd power, because the time that elapses is 2 years. 1.04² is 1.0816. That's that. Now, multiply 7,500 to find the total amount of money. 1.0816 * 7,500 is 8,112. There. Toby's savings account balance in 2 years is £8,112.
Note: To solve for compound interest questions like it, add 1 to the percentage rate in decimal form, raise that number to a power based on the number of years (for example, raise the number to the 7th power if we are looking for the balance after 7 years), and then multiply that number by the starting amount. After you raise the number by a power, there may be a lot of numbers behind it. Whatever you do, DO NOT delete the number. Keep it there and multiply it by the principal.
??? what do u mean
like numbers in the thousands place is 3
Answer:
The first choice is correct
Step-by-step explanation:
$32.00 x 15% = 4.80. 32.00-4.80=27.20. Another way to work it is the first choice, subtracting 15% from 100% and then multiplying 85% by $32.00. Same answer
