Question

you are rolling a 10-sided die with sides numbered 1-10. you keep rolling the die until you roll a prime number and then stop. let x be the number of times you roll the die. let y be the final value of the die. (a) what is e(x)?

Answer 1

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 =

$P(Prime) = \frac{4}{10}$

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.$\frac{4}{10}$ + 2. $\frac{6}{10}$.$\frac{4}{10}$ + 3.$\frac{6}{10}$.$\frac{6}{10}$$\frac{4}{10}$ + 4. $\frac{6}{10}$.$\frac{6}{10}$.$\frac{6}{10}$.$\frac{4}{10}$.......

Hence, this is the value of E(x)

To learn more about Prime number, here

brainly.com/question/9315685

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