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A bag contains 12 red balls and 8 yellow balls. Three balls are taken out of the bag and on each occasion, the ball is not returned to the bag. Find the probability of obtaining two red balls and a yellow ball in any order?
Wei Wei
In essence there are only 3 possibilities:
RRY
RYR
YRR
The sum of the odds of these three things is the possibility of one of them happening. The order does matter in this, because which one you draw first affects the odds of which one you draw second in this scenario.
There's 20 balls to begin with, and each time we remove a ball we're decreasing the total number, so the odds break down like this:
RRY:
12/20 * 11/19 * 8/18
RYR:
12/20 * 8/19 * 11/18
YRR:
8/20 * 12/19 * 11/18
Because of the specific circumstances the odds of each are actually the same (because we're decreasing the total pool and the individual pools at the same rate in all three, essentially they're the same numbers in different orders). Each has a roughly 15.2% chance, and adding those odds together gives us the odds of one of them happening (but it doesn't matter which one).
Totaling to a roughly 46.2% chance of drawing some combination of the three.
For comparison, there's a 19.2% chance that they come up as RRR, and a mere 4.9% chance that they come up YYY. The odds of two yellows and a red, meanwhile is about 29.4. Note that, because of my rounding this only totals out to 99.7%, but you get the picture. If you need the odds to a more specific decimal point, you can plug in the numbers and get the full totals.
Michael Scalise
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A class of 14 boys and 11 girls. What is the probability of selecting a girl 1st and then a girl 2nd and then a boy third.?
Assuming the choices are made randomly and that the chosen people are not returned to the class, the probability is 77/690 = 0.1116 approx.
What is the probability of not picking green if there is 10 blue 5 stripped 8 green 1 yellow 1 black?
The answer depends on how many are picked,whether they are returned after picking and whether the picking is done at random. In a single random selection the probability is 17/25.
What s the probability of not picking a green marble in a jar that contains 5 red 6 green and 4 blue?
The answer depends on how many marbles are picked and on whether or not they are returned to the jar before picking the next one. Since you have not bothered to provide any information on either of these aspects, I cannot provide a more useful answer.
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Definition of theoretical probability?
The term "theoretical probability" is used in contrast to the term "experimental probability" to describe what the result of some trial or event should be based on math, versus what it actually is, based on running a simulation or actually performing the task. For example, the theoretical probability that a single standard coin flip results in heads is 1/2. The experimental probability in a single flip would be 1 if it returned heads, or 0 if it returned tails, since the experimental probability only counts what actually happened.
What is the probability of drawing three kings in a row from a standard deck of cards when the drawn card is not returned to the deck each time?
It is 0.000181, approx.
A class of 14 boys and 11 girls. What is the probability of selecting a girl 1st and then a girl 2nd and then a boy third.?
Assuming the choices are made randomly and that the chosen people are not returned to the class, the probability is 77/690 = 0.1116 approx.
What is the probability of drawing three non face cards in a row from a standard deck of cards when the drawn card is not returned to the deck each time?
It is approx 0.41
What is the probability of not picking green if there is 10 blue 5 stripped 8 green 1 yellow 1 black?
The answer depends on how many are picked,whether they are returned after picking and whether the picking is done at random. In a single random selection the probability is 17/25.
What s the probability of not picking a green marble in a jar that contains 5 red 6 green and 4 blue?
The answer depends on how many marbles are picked and on whether or not they are returned to the jar before picking the next one. Since you have not bothered to provide any information on either of these aspects, I cannot provide a more useful answer.
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First you have 3 blues out of 13 cards, so the first card has probability 3/13. Then you have 2 blues out of 12 cards, so the second card has probability 2/12 or 1/6. The probability of both being blue is the product of these probabilities: P(two blues) = P(first blue) * P(second blue) = (3/13) * (1/6) = 3/78 or 1/26
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