Suppose 𝑋𝑖 for 𝑖 = 1,2,3 are independent and identically distributed random…

Suppose 𝑋𝑖 for 𝑖 = 1,2,3 are independent and identically distributed random variables whose probability mass functions are Pr[𝑋𝑖 = 0] = Pr[𝑋𝑖 = 1] = 1/2 for 𝑖 = 1, 2, 3. Define another random variable 𝑌 = 𝑋1𝑋2 ⊕ 𝑋3, where ⊕ denotes XOR.

Then Pr[𝑌 = 0|𝑋3 = 0] =_______________.