Final answer:
The value of p such that x1, x2, and x3 are mutually independent is 0.5.
Step-by-step explanation:
The value of p such that x1, x2, and x3 are mutually independent is 0.5.
To determine the value of p, we need to use the formula for independence in probability:
P(Y OR Z) = P(Y) + P(Z) - P(Y)P(Z).
Since the events x1, x2, and x3 are mutually independent, we can set P(x1 AND x2 AND x3) = P(x1)P(x2)P(x3) = p³.
Substituting this into the formula, we get p³ = p + p - p².
Simplifying, we have p³ - 2p² + p = 0.
Factoring the equation, we get p(p - 1)(p - 0.5) = 0.
Therefore, the possible values of p are 0, 1, or 0.5.
Since x1, x2, and x3 are independent, the value of p should be 0.5.