Answer:
The product of two rational numbers is a rational number
Step-by-step explanation:
I'll quickly recap the proof: a rational number is, by definition, the ratio between two integers. So, there exists four integers m,n,p,q such that
If we multiply the fractions, we have
Now, mp and nq are multiplication of integers, and thus they are integers themselves. So, ab is also a ratio between integer, and thus rational.
Answer:
a)
b)
And we have the following table:
X | 0 | 1 | 2
P(X) | 0.25 | 0.5 | 0.25
Step-by-step explanation:
Let's define first some notation
H= represent a head for the coin tossed
T= represent tails for the coin tossed
We are going to toss a coin 2 times so then the size of the sample size is
a. What is the sample space for this chance experiment?
The sampling space on this case is given by:
b. For this chance experiment, give the probability distribution for the random variable of the total number of heads observed.
The possible values for the number of heads are X=0,1,2. If we assume a fair coin then the probability of obtain heads is the same probability of obtain tails and we can find the distribution like this:
And we have the following table:
X | 0 | 1 | 2
P(X) | 0.25 | 0.5 | 0.25