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Independent Events
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∙ 15y ago
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What does equally unlikely mean in probability?
Two events are equally unlikely if the probability that they do not happen is the same for each event. And, since the probability of an event happening and not happening must add to 1, equally unlikely events are also equally likely,
What is the probability of flipping heads and rolling an odd number?
These would be independent events; therefore, we can multiply the probabilities of each of the two events. Probability of flipping a head: 1/2 Probability of rolling an odd number with a single die: 1/6 Required probability : 1/2 x 1/6 = 1/12
A sample space consists of 10 separate events that are equally. what is the probability of each?
I believe you mean to say, equally probable. By stating they are separate events, I assume that they are independent and that there is a single unique outcome to each event that can be identified. Ok, then the chance of each event or outcome is 1/10.
If you toss a coin 3 times what is the probability that it will land on heads 3 times?
The probability of getting heads on three tosses of a coin is 0.125. Each head has a probability of 0.5. Since the events are sequentially unrelated, simply raise 0.5 to the power of the number of tosses (3) and get 0.125, or 1 in 8.
How can you state and illustrate the addition multiplication Theorem of Probability?
Addition Theorem The addition rule is a result used to determine the probability that event A or event B occurs or both occur. ; The result is often written as follows, using set notation: : ; where: : P(A) = probability that event A occurs : P(B) = probability that event B occurs : = probability that event A or event B occurs : = probability that event A and event B both occur ; For mutually exclusive events, that is events which cannot occur together: : = 0 ; The addition rule therefore reduces to : = P(A) + P(B) ; For independent events, that is events which have no influence on each other: : ; The addition rule therefore reduces to : ; Example ; Suppose we wish to find the probability of drawing either a king or a spade in a single draw from a pack of 52 playing cards. ; We define the events A = 'draw a king' and B = 'draw a spade' ; Since there are 4 kings in the pack and 13 spades, but 1 card is both a king and a spade, we have: : = 4/52 + 13/52 - 1/52 = 16/52 ; So, the probability of drawing either a king or a spade is 16/52 (= 4/13).MultiplicationTheorem The multiplication rule is a result used to determine the probability that two events, A and B, both occur. The multiplication rule follows from the definition of conditional probability. ; The result is often written as follows, using set notation: : ; where: : P(A) = probability that event A occurs : P(B) = probability that event B occurs : = probability that event A and event B occur : P(A | B) = the conditional probability that event A occurs given that event B has occurred already : P(B | A) = the conditional probability that event B occurs given that event A has occurred already ; For independent events, that is events which have no influence on one another, the rule simplifies to: : ; That is, the probability of the joint events A and B is equal to the product of the individual probabilities for the two events.
Is the probability of two independent events occurring together the same as the probability of each occurring alone?
No, the combined probability is the product of the probability of their separate occurrances.
The probability of two independent events occurring together is the of the probability of each event occurring separately?
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What does equally unlikely mean in probability?
Two events are equally unlikely if the probability that they do not happen is the same for each event. And, since the probability of an event happening and not happening must add to 1, equally unlikely events are also equally likely,
What is a probability of tossing exactly two heads?
Coin tosses are what we call Independent Events, meaning that the results of one toss have no effect on the next toss or any thereafter. Therefore the probability of each toss is 1/2. If, however, you want to know the probability of tossing two coins, and each coin landing heads-up, you simply multiply their probabilities together, resulting in 1/4.
What is Probability of Flipping a coin five times in a row and having it land on heads?
The probability of getting a heads on the first flip is 1/2. Similarly, the probability on each subsequent flip is 1/2, since they are independent events. The probability of several independent events happening together is the product of their individual probabilities.
Why did Scrooge have 3 sprits?
Dickens gave the ghosts a theme. Ech was to take on a timeline of Scrooges life and in each time line was to opens Scrooges eyes to the events of his life and the effect those events had on him and others
A spinner with 10 equal sectors numbered 1 through 10 is spunFind the probability of each eventWrite your answer as a ratio as a decimal and as a percent?
There are ten possible events: that the spinner shows one of the number from 1 to 10. The probability of each of these events is the same and equals 1/10, 0.1 or 10%
What is the probability of winning two games with the same probability of 0.8?
The probability of winning two games with the same probability of 0.8 can be calculated by multiplying the probability of winning the first game (0.8) by the probability of winning the second game (0.8). Therefore, the probability is 0.8 * 0.8 = 0.64, or 64%.
What is the probability of flipping heads and rolling an odd number?
These would be independent events; therefore, we can multiply the probabilities of each of the two events. Probability of flipping a head: 1/2 Probability of rolling an odd number with a single die: 1/6 Required probability : 1/2 x 1/6 = 1/12
What is discrete probability and what role could it play in your work environment?
Discrete probability is probability in the context of random variables that can only take a discrete number of values. In the work environment there are some events that can have discrete outcomes and others that are continuous. For example, the number of customers in a day (or month) is a discrete variable. The amount that each one spends on your products is discrete. But the time interval between them is not. So the role that any kind of probability could play depends on what you wish to study.
A sample space consists of 10 separate events that are equally. what is the probability of each?
I believe you mean to say, equally probable. By stating they are separate events, I assume that they are independent and that there is a single unique outcome to each event that can be identified. Ok, then the chance of each event or outcome is 1/10.
What is the probability of drawing a card from each of 2 decks and getting the two of clubs from both decks?
Let's say there are 52 cards in a deckThere's one chance out of 52 to get the two of clubs from the first deckThe same chance with the second deckThe probability that the two events occur at the same time is the probability of the first multiplied by the probability of the second as the events are independentSo P = 1/52 x 1/52 = 1/2074
