Max Below a Threshold

The maximum is below $0.8$ exactly when all three variables are below $0.8$.

Use independence to multiply the three individual probabilities.

1. 1. Rewrite the event

   $\max (X_1,X_2,X_3)<0.8$ if and only if every $X_i<0.8$.

2. 2. Multiply independent probabilities

   $P={\left(0.8\right)}^3=0.512$.

   $$P=0.8^3=0.512$$

Answer: 0.512