Question 1:
A die is rolled twice and afterwards – a coin is tossed once.
- What’s the chance to get at least once “1” and also heads?
- If we got “4” once, what’s the chance that the total is “9”?
- If we didn’t get “6”, what’s the chance the total of the 2 rolls is “6”?
- Are the events “we got tales” and “the sum isn’t 6” are independent from one-another or dependent?
Answer 1:
- That’s the probability:
- That’s the probability:
- That’s the probability:
- Chance for tales = 0.5. Chance for sum isn’t 6 is 1 minus the chance for sum=6, which is
One result has no effect on the other, so we get that:
so the events are independent.
Question 2:
In front of us there’s a bowl with 10 red marbles, 15 white marbles and 11 blue marbles.
- We take 3 marbles without replacement. What’s the chance both of them had the same color?
- Assume that we pull 2 marbles without replacement, and “x” is a random variable, counting the number of white marbles. What’s the expected value of the variable “x”?
- What’s the standard deviation of the variable Y=2x-6?
- Assume that we draw 5 marbles with replacement. What’s the chance we got only one red marble?
Answer 2:
Totally we have 36 marbles.
- That’s the probability:
- That is the relevant probability function:
So the expected value is:
- For the transformation we need the standard deviation of x:
And the standard deviation of the transformation is:
- The chance for a single red marble is 10/36. So the chance for only 1 marble is:
