How many outcomes are there in the sample space for rolling one die

36

6

1

12

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How many outcomes are there in the sample space for rolling one die

36

6

1

12

1. 7 outcomes.

2. 64 outcomes.

3. D and H

Step-by-step explanation:

1. The experimenter will record the total number of heads after flipping the coin 6 times, therefore, the possible outcomes are: the experimenter got 0 heads, the experimenter got 1 head,..., the experimenter got 6 heads. Therefore there are 7 possible outcomes: (0, 1, 2, 3, 4, 5, 6).

2. If the experimenter records the result after each flip (H or T), for the first flip she has 2 results (heads or tails), for the second one she has 2 results, same for the third, fourth, fifth and sixth flip.

Therefore the possible outcomes are: [tex](2)(2)(2)(2)(2)(2)=2^{6}=64[/tex].

3. Now the experimenter will end up the experiment earlier if she gets two tails or two heads in a row.

A.TTHTT is not possible because in this case she would've ended up the experiment after the second flip since she got two tails.

B.TTH is not possible either for the same reason.

C. HT is not possible because she still needs to get another T or two H in a row.

D. This is a possible outcome because in this one she flipped the coin 6 times and she didn't get two heads or two tails in a row so she didn't finish it earlier.

E. Is not possible because she should've stopped after the second flip.

F. Is not possible because it has 7 letters, therefore, 7 flips.

G. Is not possible because she should've stopped once she got heads in the fourth and fifth flip.

H. Is possible because she got heads in the second and third flip.

the answer is 36

There are 4 outcomes

Step-by-step explanation:

cuz 2*2=4

6

Step-by-step explanation:

There are 36 outcomes possible

Ultimately, one can define one's events and sample space however one wants. But we usually design it with some sort of problem in mind. You can understand it by assuming that 1 coin is red and the other is black. In this case there are exactly 4 outcomes when you flip these 2 coins, that is HH, HT, TH or TT.

Assuming there are 6 sides on the dice, then there are 36 different outcomes

The 36 comes from the result of 6*6 = 36

If you want, you can draw out a table that has 6 rows and 6 columns. There will be 36 cells which are the results of adding any two combinations of the two dice.

The answer is 336.

Sol'n:

8P3 = 336 ways

where P = permutation

We use Permutation rather than Combination.

In the problem, it asks for the outcome or ways. Pablo picked 3 marbles over the eight marbles but it didn't mention if he picked a yellow, green, or red marble. In this state, you are going to assume that he picked random color of marbles. In that case, you are going to use Permutation.