Solution:

Joey sold 15 ice creams that day.

The fourth kid bought a single ice cream. Therefore, we have the following equation:
Total - (Total / 2 + 1/2) = 1
Solving it, we get the total as 3.

Let's work this method till we reach the first kid.

The first kid bought 15 / 2 + 1/2 = 8 (leaving 7)
The second kid bought 7 / 2 + 1/2 = 4 (leaving 3)
The third kid bought 3 / 2 + 1/2 = 2 (leaving 1)
The fourth kid bought 1 / 2 + 1/2 = 1

Adding all of them together, we get
8 + 4 + 2 + 1 = 15.

Solution:

80

Explanation:
21 B 7 C 9 D 10 A 13
= 21 / 7 + 9 X 10 - 13
= 3 + 90 - 13
= 80

Solution:

The total number of students is 500.

To follow how and why, please see the venn diagram.

Solution:

The best way to increase the probability of winning is to place one yellow ball in the first bowl and all the other balls in the second bowl.

Now, you have a 1/2 probability of choosing the bowl with just one yellow ball. If you choose that, you win.

If you choose the other bowl, it has 49 yellow balls and 50 white balls. You still have almost 1/2 probability of picking a yellow ball out of it and winning.

Solution:

2nd

When the cylinder is spun for the first and last time, the following six outcomes are possible:

First:
First chamber is fired first. The first player loses.

Second:
Second chamber is fired first. The first player loses.

Third:
Third chamber is fired first. The first player loses.

Fourth:
Fourth chamber is fired first. The second player loses. (First shot, player 1, chamber 4 empty. Second shot player 2, chamber 5, empty. Third shot player 1, chamber 6 empty. Fourth shot player 2, chamber 1 not empty.)

Fifth:
Fifth chamber is fired first. The first player loses. (First shot, player 1, chamber 5 empty. Second shot player 2, chamber 6, empty. Third shot player 1, chamber 1 not empty.)

Sixth:
Sixth chamber is fired first. The second player loses. (First shot, player 1, chamber 6 empty. Second shot, player 2, chamber 1, not empty)

Thus, if you analyze, you will find that the second player has a 4/6 chance of winning. Therefore if you want to win the game, going second gives you better shot at it.

Solution:

Both S and T are of same height because they are the same people.

Suppose that each person is marked with their respective number which also denotes their height.
Now when the longest from each row is called out, they will be 50, 100, 150 ... 500. Shortest among them will be 50 aka S.
When the shortest from each colum is called out, they will be 1, 2, 3, ....50. Longest among them will be 50 aka T.

Thus, they both are same person.

Solution:

75km

Explanation:
Distance between Bill and Darren = 40 km
Distance between Bill and Chris + Distance between Chris and Darren = 40 km
Distance between Bill and Chris + (Distance between Bill and Chris - 10) = 40 km
2 * Distance between Bill and Chris = 50 km
Distance between Bill and Chris = 25
Distance between Chris and Darren = 15 km

Therefore, distance between Darren's house and Alex's house = 60 + 15 = 75 km.

Solution:

19

Explanation:
The children can purchase 19 chocolates in return.

Out of 77 wrappers, 75 will be used to buy 15 chocolates and two will be left spare.
The 15 chocolates will create 15 empty wrappers that can be exchanged to get three chocolates.
Three chocolates will return three wrappers which will help them buy another chocolate.
Now the wrapper from this chocolate and the two spare that were left earlier will get them another chocolate.
15 + 3 + 1 = 19

Solution:

If all other conditions are fair, then the toss will generate a 52:48 distribution in the favor of heads. The toss boas factor will then be 52/48.

Using the same approach, if the coin will generate a 49:51 distribution in the favor of tails, the coin bias factor for heads will be 49/51.

Using the results, we can say that the combined bias factor is (52 * 49) / (51 * 48) = 2548 / 2448 which can be canceled if the floor bias factor is 2448 / 2548. The floor will generate a distribution factor of 2448 / (2558 + 2448) : 2548 + 2448) in favor of tails. If you calculate roughly, it will be 51.00080064% tails.

Solution:

According to the given data,

6 x number of notebooks + 5 x number of notepads = 32

Here, we are sure that the number of notebooks and the number of notepads can only result in whole numbers. Thus, the respective values will be 2 and 4.