Probability Of Simple And Compound Events

Since the bag contains only blue buttons, there are no red buttons to pick from. Therefore, the probability of picking a red button from the bag is 0.

The answer is "Dependent" because the probability of choosing the second cube depends on the outcome of the first cube. Since the first cube is not replaced, the composition of the bag changes after each draw. Therefore, the probability of selecting a certain color cube for the second draw is affected by the removal of the first cube.

The statement is true because probabilities represent the likelihood of an event occurring, and they can only range from 0 to 1. A probability of 0 means that the event will not occur, while a probability of 1 means that the event is certain to occur. Any value outside of this range would not make sense in the context of probabilities. Therefore, the statement is correct.

The coin toss and rolling the die are independent events because the outcome of one event does not affect the outcome of the other event. The result of obtaining a head on the coin toss has no impact on the result of obtaining a 5 on the die roll.

The given scenario involves spinning a number 6 and then spinning a number 5 on the same spinner. These events are considered independent because the outcome of spinning a number 6 does not affect the outcome of spinning a number 5. The probability of spinning a number 6 and the probability of spinning a number 5 are not dependent on each other.

The experimental probability of spinning an 8 is 13/100 because out of the 100 spins, the number 8 appeared 13 times.

There are a total of 15 cards, out of which 8 are odd-numbered (1, 3, 5, 7, 9, 11, 13, 15). Therefore, the probability of choosing an odd-numbered card is 8/15.

Taking a colored ball from a basket and drawing another ball without replacement are dependent events. This is because the outcome of the second event is influenced by the outcome of the first event. When a ball is taken from the basket, the total number of balls in the basket decreases, which affects the probability of drawing a specific ball on the second draw.

The correct answer is 12/15. Since there are 15 coins in total and 3 of them are Chinese yuan, there are 12 coins that are not Chinese yuan. Therefore, the probability of picking a coin that is not Chinese yuan is 12/15.

The correct answer is 0 and 0.5 because a probability value between 0 and 0.5 indicates that the event is unlikely to happen. A probability of 0 means that the event will not occur at all, while a probability of 0.5 means that there is a 50% chance of the event happening. Therefore, something that is unlikely to happen falls within this range of probabilities.

The probability of selecting a queen from a standard 52-card deck is 4/52, as there are 4 queens in the deck. The probability of selecting a 3 is also 4/52, as there are 4 threes in the deck. Since we are interested in the probability of selecting either a queen or a 3, we can add these two probabilities together to get 8/52 or 2/13.

When flipping a fair coin twice, there are four possible outcomes: heads-heads, heads-tails, tails-heads, and tails-tails. Since each flip is independent, the probability of getting heads on the first flip is 1/2, and the probability of getting heads on the second flip is also 1/2. Therefore, the probability of getting heads on both flips (heads-heads) is (1/2) * (1/2) = 1/4.

The events are ordered from least likely to most likely to occur. The event that has no chance of happening (c) is the least likely, followed by the event that could happen but is unlikely (d). The event that is just as likely to happen as not to happen (b) is next, followed by the event that is likely to happen (e). Finally, the event that is certain to happen (a) is the most likely to occur.

When you pick a marble at random, there are a total of 12 marbles in the bag. Out of these 12 marbles, 5 are green and 3 are orange. After putting the first marble back, the total number of marbles remains the same. Therefore, when you select the second marble at random, the probability of getting a green marble is still 5/12. Since both events are independent, the probability of getting both a green and an orange marble is the product of their individual probabilities, which is (5/12) * (3/12) = 5/48.

When selecting a card at random without replacement, the probability of selecting the letter "M" first is 1 out of the total number of cards, which is 55. After selecting the "M" card, there are now 54 cards left, and the probability of selecting the letter "H" second is 1 out of 54. Therefore, the probability of selecting "M" first and then "H" second is 1/55 multiplied by 1/54, which simplifies to 0.0181.