We have a deck of 10 cards numbered from 1 to 10. Some are grey and some are white. The cards numbered 1, 7, and 9 are grey. 12 3 4 5 6 7 8 9 10 The cards numbered 2, 3, 4, 5, 6, 8, and 10 are white. A card is drawn at random. Let X be the event that the drawn card is grey, and let P(X) be the probability of X. Let not X be the event that the drawn card is not grey, and let P(not X) be the probability of not X. (a) For each event in the table, check the outcome(s) that are contained in the event. Then, in the last column, enter the probability of the ever Outcomes Event Probability 123 4 5 6 7 8 9 10 O|口1□|□|□ P(x) = [] 口|ロ|□|C not X 口口|口|□|□|□|□|□|□1□ P(not X) = ] (b) Subtract. 1-P (not X) = ]
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.
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O PROBABILITY
Probabilities of an event and its complement
We have a deck of 10 cards numbered from 1 to 10.
Some are grey and some are white.
The cards numbered 1, 7, and 9 are grey.
1 2 3 45 6 7 8 9 10
The cards numbered 2, 3, 4, 5, 6, 8, and 10 are white.
A card is drawn at random.
Let X be the event that the drawn card is grey, and let P(X) be the probability of X.
Let not X be the event that the drawn card is not grey, and let P(not X) be the probability of not X.
(a) For each event in the table, check the outcome(s) that are contained in the event. Then, in the last column, enter the probability of the event
Outcomes
Event
Probability
1
23 4 5 6 7 8 9 10
口|口|□|C10|□|□|□1□1□
P(x) = ]
口|口|口|□|□|□1□||□|□
P(not X) = ]
not X
(b) Subtract.
- P (not X) = []
Explanation
Check
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![not X
P(not X) = ]
(b) Subtract.
1 – P(not X) = [.
(c) Select the answer that makes the sentence true.
1-P(not X) is the same as (Choose one)
Explanation
Check
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We have given that,
A deck of 10 cards numbered from 1 to 10. There are two colors one is grey and other one is white.
There are 3 grey color cards of numbered 1, 7 & 9.
And 7 white color cards of numbered 2, 3, 4, 5, 6, 8 & 10.
Let X be the event that the drawn card is grey and not X be the event that is not grey.
Probability = (Number of favourable cases) / ( Exhaustive cases )
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