The formula for E(x) would be SUM[ X(n)P(n)] from n = 1 to n = infinity until we get the prime number 
In the given problem, a 10-sided die with 1-10 numbers is rolled until we get a prime number 
Prime numbers between 1-10 = 2,3,5,7 (4 prime numbers)
Non - prime numbers = 1,4,6,8,9,10( 6 non-prime number)
Let X be the number of times the die is rolled 
The probability of getting a prime = 

Now, the value of 
E(X)=∑x.P(x) [ x-> {1, infinity}]
= P(1)X(1) +P(2)X(2)+P(3)X(3)+P(4)X(4)........+ P(n)X(n)
= 1. + 2.
 + 2.  .
. + 3.
 + 3. .
.
 + 4.
 + 4.  .
. .
. .
. .......
.......
Hence, this is the value of E(x) 
To learn more about Prime number, here
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