Question: A company has 3 security guards(A,B and C). Guards A and B form a patrolling team (Team 1) and guard C alone forms another patrolling

A company has 3 security guards(A,B and C). Guards A and B form a patrolling team (Team 1) and guard C alone forms another patrolling team (Team 2). Each team carries a pager activated by sensors. Both teams independently report any alert, but only 1 guard in a team will report an alert. The probability that A or C reports an alert is 0.55 and that B or C reports an alert is 0.475.

(i) Given the probability that at least one guard will report an alert is 0.775. Determine the probability of A reporting an alert, the probability of B reporting an alert and the probability of C reporting an alert.

(ii) Now the company employs another guard (D) to join Team 2. The probability of guard D reporting an alert is 0.35. Determine the probability that at least one team will report an alert.

(iii) Given that team 2 (comprises guards C and D) reports an alert, what is the probability that guard A reports an alert?

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