Pr(Red or Blue) = 0.5833...Pr(R on first pull and Blue on second pull) = 0.0533...
2/13
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%.
Bag with 10 marbles: 3 orange, 5 black, 2 white.Rephrasing the question.If a marble is drawn from the bag, then returned to the bag, and a second marbleis drawn, what is the probability that the first marble turns out white and the secondmarble black ?The probability for a marble to come out white from the bag is:P(W) = 2/10 = 1/5The probability for a marble to come out black from the bag is:P(B) = 5/10 = 1/2The probability for a marble to come out white, put back in the bag and then take again a marble for a second time and turns out to be black is:P(B2|W1) = (1/5)∙(1/2) = 1/10 = 0.10 = 10 %
The maximum number of marbles you have to draw is three. 1) Draw a marble. It is either white or black. 2) Draw a second marble. If it is the same colour as the first marble, we are done after two draws. 3) Otherwise, the drawn marbles have different colours. Draw a third marble. No matter what you draw next, you must have two marbles of the same colour.
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
The odds of pulling a red marble on the first try is 4/15 or about .27 and the probability of drawing a white marble the second time if a the first is a red marble is 5/14 or about .36. the odds of both happening is the product of the probabilities of the other events, or 2/21.
There are 13 marbles in total. The order is specified.P(1st is white and the 2ndis purple) = (7/13)(6/12) = (7/13)(1/2) = 7/26.
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.
3/5
2/13
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%.
Probability of drawing a blue marble first is 4 in 8 (or 50%) Probability of drawing a blue marble second is 3 in 7 (or 42.85714%) Probablility of drawing blue then blue is the two above multiplied 0.5 * 0.4285714 Which is 0.212142407 or 21% or One in Five.
Bag with 10 marbles: 3 orange, 5 black, 2 white.Rephrasing the question.If a marble is drawn from the bag, then returned to the bag, and a second marbleis drawn, what is the probability that the first marble turns out white and the secondmarble black ?The probability for a marble to come out white from the bag is:P(W) = 2/10 = 1/5The probability for a marble to come out black from the bag is:P(B) = 5/10 = 1/2The probability for a marble to come out white, put back in the bag and then take again a marble for a second time and turns out to be black is:P(B2|W1) = (1/5)∙(1/2) = 1/10 = 0.10 = 10 %
12 white marbles from (7+3+12) = 22 marblesChance of a white marble on first pick = 12/22 = 6/11.Chance of a white marble on second and third picks are the same, as the marble is replaced.So, the chance of a white marble three times is 6/11 * 6/11 * 6/11 = 216/1331 = approximately 16.23%
The maximum number of marbles you have to draw is three. 1) Draw a marble. It is either white or black. 2) Draw a second marble. If it is the same colour as the first marble, we are done after two draws. 3) Otherwise, the drawn marbles have different colours. Draw a third marble. No matter what you draw next, you must have two marbles of the same colour.
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
4/8 or 1/2(probability of first draw) * 3/8(probability of second draw which is 12/64 or 3/16 of the given scenario.