can someone help in this question
A company has a security system comprising four electronic devices
(A, B, C and D) which operate independently. Each device has a
probability of 0.1 of failure. The four electronic devices are
arranged so that the whole system operates if at least one of A or B
functions and at least one of C or D functions.
Show that the probability that the whole system functions properly
is 0.9801.
we have use probability tree need help test tomorrow please

Question

can someone help in this question 
A company has a security system comprising four electronic devices
(A, B, C and D) which operate independently. Each device has a
probability of 0.1 of failure. The four electronic devices are
arranged so that the whole system operates if at least one of A or B
functions and at least one of C or D functions.
Show that the probability that the whole system functions properly
is 0.9801.
we have use probability tree need help test tomorrow please

kropot72 · Answer

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The probability tree applies to each pair of devices, A and B, C and D.
The probability of one or both devices of a pair operates is given by
0.81 + 0.09 + 0.09 = 0.99
The probability that one or both devices in A and B, C and D operate (that is the probability that the whole system functions properly) is given by
0.99 * 0.99 = 0.9801