A fair tetrahedral die (with face 1,2,3 and 4)and a fair coin are tosses together
Construct a table of sample space of a random experiment
Use your sample space to.find the probability that
(1):a tail and an odd number show up
(2):a head and a square show up
(3): a head show up
help
just list the possible outcomes
1H
2H
3H
4H
...
how do I answer
question 1&2?
well, if you have made the table, just count how many total outcomes there are
Then count the number of successes appear in the list
probability is #success/#total
sometimes that isn't easy to determine, but here the list is quite small.
hummmm
hummmmmmm
Sure, I'll help you with that! Here's the table of the sample space for the random experiment of tossing a fair tetrahedral die and a fair coin together:
Coin | Tetrahedral Die
-------------------------
Head | 1
Head | 2
Head | 3
Head | 4
Tail | 1
Tail | 2
Tail | 3
Tail | 4
Now let's find the probabilities:
(1) To find the probability of getting a tail and an odd number, we look for the outcomes where the coin shows a tail and the tetrahedral die shows an odd number. In this case, there is only one outcome: Tail and 1. So the probability is 1/8 or 0.125.
(2) To find the probability of getting a head and a square number, we look for the outcomes where the coin shows a head and the tetrahedral die shows a square number. Since there are no square numbers on the tetrahedral die, there are no such outcomes. So the probability is 0.
(3) To find the probability of getting a head, we look for the outcomes where the coin shows a head. There are four outcomes: Head and 1, Head and 2, Head and 3, Head and 4. So the probability is 4/8 or 0.5.
I hope that helps! Let me know if you have any other questions or if you need more help with anything else!
To construct a table of the sample space for this experiment, we can list all the possible outcomes by combining the outcomes of the coin toss (heads or tails) with the outcomes of the die roll (numbers 1, 2, 3, or 4).
The sample space for this experiment consists of the following outcomes:
1. Heads and 1
2. Heads and 2
3. Heads and 3
4. Heads and 4
5. Tails and 1
6. Tails and 2
7. Tails and 3
8. Tails and 4
Now let's calculate the probabilities for the given events:
(1) To find the probability of getting a tail and an odd number, we need to count the number of outcomes that satisfy this condition and divide it by the total number of outcomes in the sample space.
Outcomes that satisfy the condition: Tails and 1, Tails and 3
Total number of outcomes: 8 (since there are 2 possibilities for the coin and 4 possibilities for the die)
The probability of getting a tail and an odd number is 2/8, which simplifies to 1/4 or 0.25.
(2) To find the probability of getting a head and a square, we need to count the number of outcomes that satisfy this condition and divide it by the total number of outcomes in the sample space.
Since there are no squares on the die, we cannot have an outcome with a head and a square. Therefore, the probability of this event is 0.
(3) To find the probability of getting a head, we need to count the number of outcomes where a head shows up and divide it by the total number of outcomes in the sample space.
Outcomes where a head shows up: Heads and 1, Heads and 2, Heads, and 3, Heads, and 4
Total number of outcomes: 8
The probability of getting a head is 4/8, which simplifies to 1/2 or 0.5.
So, to summarize:
(1): The probability of a tail and an odd number showing up is 1/4 or 0.25.
(2): The probability of a head and a square showing up is 0.
(3): The probability of a head showing up is 1/2 or 0.5.
Remember, the sample space provides a comprehensive list of possible outcomes, and probabilities are calculated by dividing the number of favorable outcomes by the total number of outcomes.