Expected value of discrete random variable

Stacy noticed that the casino "Trap" uses an unusual dice: not all faces have the same probability of falling out. Stacy was able to establish that the probability of an even number falling out is $0.6$; the probability of a number divisible by $3$ falling out is $0.3$; the probability of a $1$ or $5$ falling out is $0.22$; the probability of a power of two (including zero power) falling out is $0.59$; the probability of a square of some number falling out is $0.24$.

Calculate the mathematical expectation of the points obtained from one roll of such a strange dice.

Tip: First, calculate the probability of each of the numbers from $1$ to $6$ falling out.