An experiment consists of first rolling a die and then tossing a coin.
How many elements are there in the sample space?
12
Let A be the event that either a 1, 2, 3 or 4 is rolled first, followed by landing a tail on the coin toss.
P(A) = Present your answer as a decimal rounded to four decimal places.
I've calculated my sample space, but I don't know how to go about the second question. What formula would I use?
Thanks in advance.
To calculate the probability of event A, you need to determine the number of favorable outcomes for event A and divide it by the total number of possible outcomes in the sample space.
In this case, event A occurs when either a 1, 2, 3, or 4 is rolled first, followed by landing a tail on the coin toss.
To calculate the number of favorable outcomes for event A, you need to count the number of outcomes that satisfy the conditions. In this experiment, a favorable outcome occurs when the die shows a 1, 2, 3, or 4 first (4 possibilities), and the coin toss results in a tail (1 possibility).
Therefore, the number of favorable outcomes for event A is 4 (the number of possibilities for the die) times 1 (the number of possibilities for the coin toss), which equals 4.
Now, let's calculate the total number of possible outcomes in the sample space. In this experiment, rolling a die can result in any number from 1 to 6, and tossing a coin can result in either a head or a tail.
Therefore, the total number of possible outcomes in the sample space is 6 (the number of possibilities for the die) times 2 (the number of possibilities for the coin toss), which equals 12.
To find the probability of event A, you need to divide the number of favorable outcomes for event A by the total number of possible outcomes in the sample space.
P(A) = Number of favorable outcomes / Total number of possible outcomes
P(A) = 4 / 12
P(A) = 0.3333 (rounded to four decimal places)
So, the probability of event A is 0.3333.
To calculate the probability of an event, you can use the formula:
P(A) = Number of outcomes in event A / Total number of outcomes in the sample space
In this case, A is the event that either a 1, 2, 3, or 4 is rolled first, followed by landing a tail on the coin toss. Let's calculate the probability step-by-step.
First, let's determine the total number of outcomes in the sample space. Since a die has 6 sides and a coin has 2 sides, the total number of outcomes is 6 (number of die outcomes) multiplied by 2 (number of coin outcomes), resulting in 12 outcomes.
Now, let's count the number of outcomes that satisfy event A. We want to roll a 1, 2, 3, or 4 first, followed by landing a tail on the coin toss.
There are 4 possible outcomes for the roll of the die, which are: {1, 2, 3, 4}.
For each of these 4 outcomes, there is only one possible outcome for the coin toss, which is a tail.
Therefore, the number of outcomes in event A is 4.
Now, let's plug these values into the formula:
P(A) = Number of outcomes in event A / Total number of outcomes in the sample space
= 4 / 12
= 1/3
Rounded to four decimal places, the probability P(A) is approximately 0.3333.
So, P(A) = 0.3333.
I hope this helps! Let me know if you have any further questions.