For safety reasons, four different alarm systems were installed in the vault containing the safety deposit boxes at a Beverly Hills bank. Each of the four systems detects theft with a probability of .99 independently of the others.1.) What is the probability that when a theft occurs, all four systems will detect it?(a) (.99)4(b) (.99) * 4(c) (.01)4(d) (.01) * 4(e) None of the above.

Answer:[tex]0.99^4[/tex]Step-by-step explanation:We are given Each of the four systems detects theft with a probability of .99 independently of the others.Let the four systems be A , B , C and D Probability of detecting theft by A = 0.99Probability of detecting theft by B = 0.99Probability of detecting theft by C = 0.99Probability of detecting theft by D = 0.99Since A , B , C and D  are independent So,The probability that when a theft occurs, all four systems will detect it = [tex]P(A) \times P(B) \times P(C) \times P(D) = 0.99^4[/tex]Hence The probability that when a theft occurs, all four systems will detect it  is [tex]0.99^4[/tex]