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If you pull 35 marbles without replacement, the answer is 1: the event is a certainty. If you pull only one marble, at random, the probability is 16/50 = 8/25.
The first marble is the independent event because its probability is only based on the sample space of the bag. The second marble is the dependent event because its probability is based on the sample space of the bag which has now been changed by the first marble.
When you are asked what is the probability of drawing "thing a" when you have only the same amount of "thing b," is called an equally likely event. For example: In a hat you have 8 black marbles and 8 black marbles. Since there the same amount of both, the chance of picking a black marble is 50% and picking a blue marble is 50%. This is an equally likely event.
It depends what probability exactly you want to find.probability = number of successful ways / total number of waysIf the problem is:You have a bag containing 4 blue, 5 red, 1 green, 2 black marble what is the probability of picking a blue marble at random?Thensuccessful ways = 4 as there are 4 blue marblestotal ways = 12 as there are 4 [blue] marbles + 5 [red] marbles + 1 [green] marble + 2 [black] marbles = 12 marbles in total.pr(picking a blue) = 4/12 = 1/3Perhaps the problem is:You pick 2 marbles at random without replacing them, what is the probability that they are the two black marbles?Each picking of a marble is an event and the two events are independent (in the sense that whatever you pick first does not affect the probability of the second pick) so you multiply the probability of each together:pr(1st black) = 2/12 = 1/6pr(2nd black) = 1/11 (there is 1 less black marble in the bag)pr(2 blacks) = 1/6 × 1/11 = 1/66Perhaps it is:You pick 2 marbles at random replacing the marble after the first pick, what is the probability of picking the same colour each time?This time there are 4 possible colours and the probabilities of 2 marbles the same is calculated for each (similar to above) and then they are added together to find the total probability of 2 marbles of the same colour:pr(blue) = 4/12 → pr(2 blue) = 4/12 × 4/12 = 16/144pr(red) = 5/12 → pr(2 red) = 5/12 × 5/12 = 25/144pr(green) = 1/12 → pr(2 green) = 1/12 × 1/12 = 1/144pr(black) = 2/12 → pr(2 black) = 2/12 × 2/12 = 4/144→ pr(2 the same colour) = pr(2 blue) + pr(2 red) + pr(2 green) + pr(2 black)= 16/144 + 25/144 + 1/144 + 4/144 = 46/144 = 23/72And so on.
The answer depends on the probability of WHICH event you want to find!
If you pull 35 marbles without replacement, the answer is 1: the event is a certainty. If you pull only one marble, at random, the probability is 16/50 = 8/25.
The first marble is the independent event because its probability is only based on the sample space of the bag. The second marble is the dependent event because its probability is based on the sample space of the bag which has now been changed by the first marble.
If you pick only one marble from the bag, at random, it can be any one of 26 marbles. Out of these, 5 of the marbles are green. Thus, there are 26 possible outcomes out of which 5 are favourable - to the event that the marble is green. Therefore the probability of a green marble is 5/26. The calculations become more complicated if you consider choosing a green marble in several attempt: it depends on whether or not the marbles are replaced before the next one is picked.
5 marbles. 3 red marbles, 2 white marbles.The probability of drawing a white marble is P(W) = 2/5 = 0.40If the white marble is not returned to the rest of the marbles (no substitution), theprobability that the second marble drawn is a red one is P(R) = 3/4 = 0.75.The probability that the event of drawing first a white marble and without substitutionthe second draw turns a red marble is P(1stW,2ndR) = (2/5)∙(3/4) = 6/20 = 3/10 = 0.30 = 30.0%.If the process of drawing the marbles is with substitution, the probability of thesecond draw turning a red marble is P(R) = 3/5 = 0.60 = 60.0%The probability that the event of first drawing a white marble and after returning themarble back to the original group of marbles (with substitution) the second draw turns a red marble is P(1stW,2ndR) = (2/5)∙(3/5) = 6/25 = 0.24 = 24.0%.
When you are asked what is the probability of drawing "thing a" when you have only the same amount of "thing b," is called an equally likely event. For example: In a hat you have 8 black marbles and 8 black marbles. Since there the same amount of both, the chance of picking a black marble is 50% and picking a blue marble is 50%. This is an equally likely event.
Because you are replacing the marbles then it is an independent event. P(1st one is not green) = 1 - P(first green), equally P(2nd one is not green) = 1 - (second green), Thus it reads P(¬G ^ ¬G) = P(¬G) * P(¬G) = 15/20 * 15/20 = 225/400 = 9/16
If the outcomes of a trial or experiment are all equally likely then the probability ratio for a specific event is the ratio of the number of outcomes that are favourable to the event divided by the total number of possible outcomes.
It depends what probability exactly you want to find.probability = number of successful ways / total number of waysIf the problem is:You have a bag containing 4 blue, 5 red, 1 green, 2 black marble what is the probability of picking a blue marble at random?Thensuccessful ways = 4 as there are 4 blue marblestotal ways = 12 as there are 4 [blue] marbles + 5 [red] marbles + 1 [green] marble + 2 [black] marbles = 12 marbles in total.pr(picking a blue) = 4/12 = 1/3Perhaps the problem is:You pick 2 marbles at random without replacing them, what is the probability that they are the two black marbles?Each picking of a marble is an event and the two events are independent (in the sense that whatever you pick first does not affect the probability of the second pick) so you multiply the probability of each together:pr(1st black) = 2/12 = 1/6pr(2nd black) = 1/11 (there is 1 less black marble in the bag)pr(2 blacks) = 1/6 × 1/11 = 1/66Perhaps it is:You pick 2 marbles at random replacing the marble after the first pick, what is the probability of picking the same colour each time?This time there are 4 possible colours and the probabilities of 2 marbles the same is calculated for each (similar to above) and then they are added together to find the total probability of 2 marbles of the same colour:pr(blue) = 4/12 → pr(2 blue) = 4/12 × 4/12 = 16/144pr(red) = 5/12 → pr(2 red) = 5/12 × 5/12 = 25/144pr(green) = 1/12 → pr(2 green) = 1/12 × 1/12 = 1/144pr(black) = 2/12 → pr(2 black) = 2/12 × 2/12 = 4/144→ pr(2 the same colour) = pr(2 blue) + pr(2 red) + pr(2 green) + pr(2 black)= 16/144 + 25/144 + 1/144 + 4/144 = 46/144 = 23/72And so on.
The answer depends on the probability of WHICH event you want to find!
The second and third marbles depend upon the first, so they are dependent. Even if they are all being drawn together, because there is no replacement, each removal affects the original group of marbles.
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