Is this true in probability? P(AUB)' = (P(A) + P(B)) '

  • Thread starter Thread starter huan.conchito
  • Start date Start date
  • Tags Tags
    Probability
AI Thread Summary
The discussion centers on the probability expression P(AUB)' = (P(A) + P(B))'. The user initially attempts to solve for P(B) using given probabilities but arrives at an impossible value of -0.5. It is clarified that this expression holds true only when events A and B do not occur simultaneously. The general formula for calculating the union of two events is provided as P{A ∪ B} = P{A} + P{B} - P{A ∩ B}. Understanding the conditions under which these probabilities apply is crucial for accurate calculations.
huan.conchito
Messages
44
Reaction score
0
Please help me with Probability

is this true in probability? P(AUB)' = (P(A) + P(B)) '

The question is
a) Assume that P(A) = 0.4 P(AnB)=0.1 P(A'nB')=0.2
P(B) = ?
what i did is:
P(AUB)= P(A)+P(B)- P(AnB)
P(AUB)= 0.4 + P(B)-0.1
P(A'nB')= 0.2 = P(AUB)' :confused: = 0.2 = 1 - (0.4 + P(B)-0.1)
P(B)= -0.5

NVM I GOT IT MYSELF
 
Last edited:
Physics news on Phys.org
Only if A and B don't occur at the same time (simultaneously)

marlon
 
what is the formula to manipulate such an expression if they occur at the same time?
 
huan.conchito said:
is this true in probability? P(AUB)' = (P(A) + P(B)) '
Here is the general form:
P{A ∪ B} = P{A} + P{B} - P{A ∩ B}


~~
 
TL;DR Summary: I came across this question from a Sri Lankan A-level textbook. Question - An ice cube with a length of 10 cm is immersed in water at 0 °C. An observer observes the ice cube from the water, and it seems to be 7.75 cm long. If the refractive index of water is 4/3, find the height of the ice cube immersed in the water. I could not understand how the apparent height of the ice cube in the water depends on the height of the ice cube immersed in the water. Does anyone have an...
Thread 'Variable mass system : water sprayed into a moving container'
Starting with the mass considerations #m(t)# is mass of water #M_{c}# mass of container and #M(t)# mass of total system $$M(t) = M_{C} + m(t)$$ $$\Rightarrow \frac{dM(t)}{dt} = \frac{dm(t)}{dt}$$ $$P_i = Mv + u \, dm$$ $$P_f = (M + dm)(v + dv)$$ $$\Delta P = M \, dv + (v - u) \, dm$$ $$F = \frac{dP}{dt} = M \frac{dv}{dt} + (v - u) \frac{dm}{dt}$$ $$F = u \frac{dm}{dt} = \rho A u^2$$ from conservation of momentum , the cannon recoils with the same force which it applies. $$\quad \frac{dm}{dt}...
Back
Top