The expected value of the winnings from the game is $4
<h3>How to determine the expected value?</h3>The payout probability distribution is given as:
Payout ($) 2 4 6 8 10
Probability 0.5 0.2 0.15 0.1 0.05
The expected value is then calculated as:
This gives
E(x) = 2 * 0.5 + 4 * 0.2 + 6 * 0.15 + 8 * 0.1 + 10 * 0.05
Evaluate the expression
E(x) = 4
Hence, the expected value of the winnings from the game is $4
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There are 26 letters in the alphabet, 5 are vowels, therefore, the probability of choosing a vowel the first time is:
and the second time is:
Continuing with this reasoning, we get that the probabilities each time are:
Finally, the probability that you get all vowels is the product of the probabilities:
Writing the above result as a percentage we get:
Answer:
Answer:
r = -16
Step-by-step explanation:
We will use "distributive" property and "adding like terms" concepts in solving for the unknown variable "r".
The distributive property is:
a(b+c) = ab + ac
So
2(10r-7) = 20r - 14
also
-2(1+10r) = -2 - 20r
So, our equation becomes:
Now we add like terms and move variables (r) to one side and numbers to another. Like terms mean:
3r + 5r = (3+5)r = 8r
So, we have:
So,
the value of r is -16