Question

This is the question ^.

On a given day, casting of concrete structural elements at a construction project depends on the availability of material. The required material may be produced at the job site or delivered from a premixed concrete supplier. However, it is not always certain that these sources of material will be available. Furthermore, whenever it rains at the site, casting cannot be performed. On a given day, define the following events: E1 = there will be no rain E2 production of concrete material at the job site is feasible E3-supply of premixed concrete is available with the following respective probabilities p(E1)= 0.8; P(E.)=0.7: P(E3)=0.95; and P(E1E2)=0.6 whereas E2 and E3 are statistically independent of E1 (a) Identify the following events in terms of E1, E2, and E3: (i) A = casting of concrete elements can be performed on a given day. (ii) B = casting of concrete elements cannot be performed on a given day. (b) Determine the probability of the event B.

This is the professor's work:

Can someone please explain to me why in the second step of (b) he did - P(E1E2E3). If the problem statement says that E1 is independent of E2E3?

Answer 1

Look at the general formulae of P(A U B)

P(A U B) = P(A)+P(B) - P(A & B)

Now, if A and B are independent event, then P( A & B) = P(A)P(B)

Therfore, P(A U B) = P(A)+P(B) - P(A)P(B)

In the question its mentioned....whereas E2 and E3 are statistically independent of E1

The P(E1 & E2E3) can therefore can be written as P(E1E2E3)