Conditional Probability Questions

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ryxnnov

Economics

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Please answer these questions. I have them but not the right answer. Please help me with the right one

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2. An envelope contains three cards: a black card that is black on both sides, a white card that is white on both sides, and a mixed card that is black on one side and white on the other. You select one card at random and note that the side facing up is black. What is the probability that the other side is also black? (10 points) B = blach (both sides) we white sudos ME black conside) and white cother side) Probability that the Other side is black = 1/2 = 0.5 Because We only have and the othes card has black in both side Conclude that its 50% ( two colds blach 0.5x100-50% side so we de buys ties 3. A prisoner is to be exiled to Siberia or the Urals (a mountain chain in Russia). The chance of being sent to Siberia is 70%. The prisoner knows that if a guard in Siberia is selected random, the probability is 0.9 that he will be armed with an AN-94 machine gun, whereas the probability is 0.6 that a guard in the Urals will be armed with one. Boy's the orom a) Upon arriving, the first guard whom the prisoner sees is armed with an AN-94. What is the probability that the prisoner has been sent to Siberia? (10 points) P(A/B) = PLBIA, SPCAI) set to sibopa 70% P(BIA) PCA, )+ P(B/AJ PLA 2) Armed with AN-94 = 0.9 Gold in Urals is armed 30.6 P = (0.7) co. a) = 0.68 1680 b) Upon arriving, the first guard whom the prisoner sees is armed with an AN-94. What is the probability that the prisoner has been sent to the Urals? (10 points) Pe 10.33/0.6); 0.18 0,18x1vo 1180 c) Find the probability that a randomly selected guard will be armed with an AN-94. (10 points) DIBIA) PLAJ) e/A/R)= 0.81 or { l/B(A).All 2.81x10 or 181% 4. A system is made up of two subsystems, A and B connected in parallel. Subsystem A is made up of 5 components connected in parallel. Subsystem B is made up of 5 components connected in-series. All components function inde- pendently. The probability that a component is operational is 0.7. Let P(S) denote the probability that the system is operational Independence a) Find P(S). (15 points) Independence of two events & PCANB) = P(A/B) DCB) Le A dorneste the event that component works (1, 2, 3, 4.a) Event the suston works as PCA, VAUA 3V ALu As) = P(A1) + P(A₂) + P(A3) + P(Au) + P(AS) - SCARPCA) PCANILAUDICAs) p(s) : 0.9 + 0,7+0,740.9+ 0.7. (2017) (0.7)(0-7)(0.7)/0,-))) 3.5 - o. 16807 Colways!) pesustom) =13.83+ 3.332 (probability 51 Coo108)-(3133) combination B) 095 = 16801 6) A component from subsystem A is tested and found to be operational. Find P(S). (10 points) PCANB) in P(A/B) = PCB) Co-1667) oindependent 20.938] Patrollel P = Co. 7)x5 - 3.33 .8 2. c) A component from subsystem B is tested and found to be operational. Find P(S). (10 points) In series 5 P = 10.9) -O. 16807 Bonus. (10 points) A component is randomly selected (from A or B, equally likely) and found to be operational. Find P(S). P/A/B) - P (B1A)'(A) EDO BAJOPA +3 i (3,33) (0.16807) : 0,5597 55.96
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2. An envelope contains three cards: a black card that is black on both sides, a white card
that is white on both sides, and a mixed card that is black on one side and white on the
other. You select one card at random and note that the side facing up is black. What is the
probability that the other side is black?
Given that the shown face is black, for the other face to be black, it must be the black
card.

P(B|A) = If the black card is drawn, a black face is shown with probability 1.
P(B) = The total probability of seeing a black face is 1/...


Anonymous
This is great! Exactly what I wanted.

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