That's the probability that both events will happen, possibly even at the same time.
I think it's called the 'joint' probability.
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.
The probability of drawing the Ace of Spades on the first draw is 1 in 52. The probability of drawing the Queen of Hearts on the second draw is 1 in 51. The probability of both of those event occurring is 1 in 2652. (1 in 52) times (1 in 51)
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 rolling a 6 the first time and a 1 the second time
The first event is Less than 4, which is either 1, 2, or 3. The probability of this is 1/2.The second event is die number = 5. The probability of this is 1/6.Multiply the two probabilities together: (1/2)*(1/6) = 1/12 (about 8.33 % chance).
They are independent, because the probability of the first event does not affect the probability of the second event.
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.
The probability of drawing the Ace of Spades on the first draw is 1 in 52. The probability of drawing the Queen of Hearts on the second draw is 1 in 51. The probability of both of those event occurring is 1 in 2652. (1 in 52) times (1 in 51)
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%.
If it's an independent event then it's probability does not depend on preceding events. For example, if I flip a coin twice the probability that the coin will show 'heads' the second time is independent of what happened the first time; it's just 1/2.
Since there are 6 sides on every die that are equally likely to be rolled, the probability of rolling any given side once is exactly 1/6. The 2 events or the first and second dice roll are independent (the outcome of one does not influence the other) so to find the probability of both occurring you just multiply the probability of each event. Since each event has a 1/6 probability of occurring as stated before, The entire event has a probability of 1/6*1/6 or 1/36, which is approximately 2.78%.
What is the probability of rolling a 6 the first time and a 1 the second time
If the two events are independent then the probability of them both happening is Pr(event1) X Pr(event2). Which in your case is 0.75x0.50=0.375 which translates into 37.5%
The first event is Less than 4, which is either 1, 2, or 3. The probability of this is 1/2.The second event is die number = 5. The probability of this is 1/6.Multiply the two probabilities together: (1/2)*(1/6) = 1/12 (about 8.33 % chance).
The probability that the second coin matches the first is 0.5 .The probability that the third coin matches the first is 0.5 .The probability that the second and third coins both match the first is (0.5 x 0.5) = 0.25 = 25%
The occurrence of one event does not affect the occurrence of the other event. Take for example tossing a coin. The first toss has no affect on the outcome of the second toss, so these events are independent.
odds"The odds against an event is a ratio of the probability that the event will fail to occur (failure) to the probability that the event will occur (success). To find odds you must first know or determine the probability of success and the probability of failure.Odds against event = P(event fails to occur)/P(event occurs) = P(failure)/P(success)The odds in favor of an event are expressed as a ratio of the probability that the event will occur to the probability that the event will fail to occur.Odds in favor of event = P(event occurs)/P(event fails to occur) = P(success)/P(failure)"Allen R. Angel, Christine D. Abbott, Dennis C. Runde. A Survey of Mathematics with Applications. Pearson Custom Publishing 2009. Pages 286-288.