Solution:

2/3

While tossing the coins in this case only two cases are favorable:

1) A1 (H) A2 (H)

2) A2 (H) A1 (H)

3) B1 (H) B2 (T)

4) B2 (T) B1 (H)

Since the fourth case is not feasible, the probability is 2/3.

Solution:

Four

three placed flat on the table in a triangle(touching each other) and put the fourth one on top of them in the middle.

Solution:

To make the coin float without touching it, all you need to do is add some salt or sugar to the water and stir until it dissolves. When you do this, the water becomes denser, which means it can support the weight of the coin, making it float up to the surface.

This happens because of something called buoyancy. The denser water pushes the coin upward, balancing the force of gravity that pulls the coin down. As a result, the coin floats without any contact!

So, with a simple trick, you can make the coin rise to the surface, all thanks to the science of density and buoyancy. Isn't physics fascinating?

Solution:

It can be done as shown in the picture below.

Solution:

To do this, he must be pushing the cork inside the bottle and then taking out the coin.

Solution:

Move the coins as given in the figure and you will get the required result.

Solution:

50%

Explanation:
The probability will be 50% only as it always was. The next flip of coin is not dependent on what the results were in the previous flips.

Solution:

The answer is 2. First, divide the coins into 3 equal piles. Place a pile on each side of the scale, leaving the remaining pile of 3 coins off the scale. If the scale does not tip, you know that the 6 coins on the scale are legitimate, and the counterfeit is in the pile in front of you. If the scale does tip, you know the counterfeit is in the pile on the side of the scale that raised up. Either way, put the 6 legitimate coins aside. Having only 3 coins left, put a coin on each side of the scale, leaving the third in front of you. The same process of elimination will find the counterfeit coin.

Solution:

She had a 50p coin, a 25p coin and four 10p coins.

Solution:

50%

Explanation:
When the coins are tossed there can be eight possible outcomes (2*2*2)
HHH
HTT
HTH
HHT
TTT
THH
THT
TTH

If you find out, we have only four favorable outcomes. Also, the events here are independent and thus we can calculate the probability by using these only.

Thus the probability is 50 percent.