Probability If P(A) = 0.40, P(B) = 0.80, and P(A and B) = 0.30 a)Determine wheth

Question

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

Explanation / Answer

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]

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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]

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