Find the vector equation of the line passing through the point A(1, 2, –1) and parallel to the line 5x – 25 = 14 – 7y = 35z.
Prove that if E and F are independent events, then the events E and F' are also independent.
Two events E and F are independent if
P(E ∩ F) = P(E).P(F)
Now,
P(E ∩ F') = P(E) – P(E ∩ F)
= P(E) – P(E). P(F)
= P(E)[1 – P(F)]
= P(E).P(F')
E and F' are independent events.
P(E ∩ F) = P(E).P(F)
Hence prove
A small firm manufactures necklaces and bracelets. The total number of necklaces and bracelets that it can handle per day is at most 24. It takes one hour to make a bracelet and half an hour to make a necklace. The maximum number of hours available per day is 16. If the profit on a necklace is ` 100 and that on a bracelet is ` 300. Formulate on L.P.P. for finding how many of each should be produced daily to maximize the profit? It is being given that at least one of each must be produced.