An electrical system has the switches shown in the following diagram to indicate

Question

An electrical system has the switches shown in the following diagram to indicate system operation based on the switch positions. The probability that Switch A is closed is: P[A_Closed] = 7/9 The probability the Switch B selecting the red LED or the Other LEDs is: P[B_Red] = 2/3 P[B_Other] = 3/5 The probability that the Selector switch S selects the various colored LEDs is: P[S_Blue] = 4/13 P[S_Yellow] = 2/13 P[S_Green] = 3/13 P[S_White] = 4/13 What is the probability that all the LEDs are off? b. What is the probability that the While LED is on? c. What is the probability that either the Red LED or the Green LED is on? d. Given that the Switch B is set to the "B_Other" LEDs position, what is the probability that either the Blue LED or the Yellow LED is on?

Explanation / Answer

a. All LEDs are off when A is open.

P(A_Open) = 1 - P(A_Closed) = 1 - 7/9 = 2/9

b. P(White) = P(A_Closed) * P(B_Other) * P(S_White) = 7/9 *3/5 *4/13 = 28/195

c. P(Red or Green) = P(Red) + P(Green) = P(A_Closed) * P(B_Red) +P(A_Closed) * P(B_Other) * P(S_Green)

= (7/9 * 2/5) + (7/9 * 3/5 * 3/13) = 49/117

d. P(Blue or Yellow | B_Other) = ( P(S_Blue) . P(B_Other) + P(S_Yellow) . P(B_Other) ) / P(B_Other)

= (3/5*4/13 + 3/5 * 2/13) / 3/5 = 6/13

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