a. How many elements are there in the sample space? b. Let A be the event that a green card is picked first, followed by landing a head on the coin toss. P(A) = Round your answer to 4 decimal places. c. Let B be the event that a red or blue is picked, followed by landing a head on the coin toss. Are the events A and B mutually exclusive? ONo, they are not Mutually Exclusive O Yes, they are Mutually Exclusive d. Let C be the event that a green or blue is picked, followed by landing a head on the coin toss. Are the events A and C mutually exclusive? ONo, they are not Mutually Exclusive OYes, they are Mutually Exclusive
Addition Rule of Probability
It simply refers to the likelihood of an event taking place whenever the occurrence of an event is uncertain. The probability of a single event can be calculated by dividing the number of successful trials of that event by the total number of trials.
Expected Value
When a large number of trials are performed for any random variable ‘X’, the predicted result is most likely the mean of all the outcomes for the random variable and it is known as expected value also known as expectation. The expected value, also known as the expectation, is denoted by: E(X).
Probability Distributions
Understanding probability is necessary to know the probability distributions. In statistics, probability is how the uncertainty of an event is measured. This event can be anything. The most common examples include tossing a coin, rolling a die, or choosing a card. Each of these events has multiple possibilities. Every such possibility is measured with the help of probability. To be more precise, the probability is used for calculating the occurrence of events that may or may not happen. Probability does not give sure results. Unless the probability of any event is 1, the different outcomes may or may not happen in real life, regardless of how less or how more their probability is.
Basic Probability
The simple definition of probability it is a chance of the occurrence of an event. It is defined in numerical form and the probability value is between 0 to 1. The probability value 0 indicates that there is no chance of that event occurring and the probability value 1 indicates that the event will occur. Sum of the probability value must be 1. The probability value is never a negative number. If it happens, then recheck the calculation.
![## Probability Experiment with Cards and Coin
A special deck of cards contains 8 **green** cards, 11 **blue** cards, and 6 **red** cards. When a card is picked, the color is recorded. The experiment consists of picking a card and then tossing a coin.
### Questions
**a.** How many elements are there in the sample space?
\[ \text{Answer:} \, \_\_\_ \]
**b.** Let \( A \) be the event that a green card is picked first, followed by landing a head on the coin toss.
\[ P(A) = \_\_\_ \, \text{Round your answer to 4 decimal places.} \]
**c.** Let \( B \) be the event that a red or blue card is picked, followed by landing a head on the coin toss. Are the events \( A \) and \( B \) mutually exclusive?
- \( \bigcirc \) No, they are not Mutually Exclusive
- \( \bigcirc \) Yes, they are Mutually Exclusive
**d.** Let \( C \) be the event that a green or blue card is picked, followed by landing a head on the coin toss. Are the events \( A \) and \( C \) mutually exclusive?
- \( \bigcirc \) No, they are not Mutually Exclusive
- \( \bigcirc \) Yes, they are Mutually Exclusive
### Explanation
- The experiment includes selecting a card from a deck and tossing a coin, making up the combined sample space.
- Determine probability by considering the total possible outcomes and specific favorable outcomes.
- Mutually exclusive events cannot both happen at the same time during a single trial of the experiment. Consider the definitions in questions c and d.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Faa7d06cc-49d9-4123-a8f6-306f9b65eea9%2F8e4e3d87-9442-4cc2-8876-62ecf1684cf4%2Fenemz3e_processed.jpeg&w=3840&q=75)
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