Probability If PA 040 PB 080 and PA and B 030 aDetermine

Probability

If P(A) = 0.40, P(B) = 0.80, and P(A and B) = 0.30

a)Determine whether A and B are independent. Show your calculation.

b)Determine p(A or B) =

2) The weight of a one cubic yard bag of landscape mulch is normally distributed with a mean of 40 pounds and a standard   deviation of 1 pound.

a)What is the probability that a bag will weigh less than 40 pounds?

b)What is the probability that a bag will weigh between 38 and 40 pounds?

Please provide the equation for each of the questions briefly that how you reached the answer.Do not just give the answer.

Thanks

Solution

1.

If P(A) = 0.40, P(B) = 0.80, and P(A and B) = 0.30

a)Determine whether A and B are independent. Show your calculation.

If A and B are independent,

P(A and B) = P(A) P(B)

Herem

P(A and B) = 0.30 (given)
P(A) P(B) = 0.40*0.80 = 0.32

Thus, as they are not equal, they are NOT INDEPENDENT. [ANSWER]

********************

b)Determine p(A or B) =

P(A or B) = P(A) + P(B) - P(A and B)
= 0.40 + 0.80 - 0.30

= 0.90 [ANSWER]

*******************************************

Hi! Please submit the next part as a separate question. That way we can continue helping you! Please indicate which parts are not yet solved when you submit. Thanks!