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If Mark randomly walks from point P to point R (he can only walk either rightward or upward), what is the probability that he passes through point Q?

Give your answer as a fraction.
S is the set of all ordered pairs (x, y) of integers such that -10 ≤ x ≤ 10 and -5 ≤ y ≤ 15.

Quantity A

The number of ordered pairs (x, y) in S such that x=y

Quantity B

16


Quantity A

The number of ordered triples ($$x_1$$, $$x_2$$, $$x_3$$), where $$x_1$$, $$x_2$$ and $$x_3$$ are non-negative integers such that $$x_1$$+$$x_2$$+$$x_3$$=9

Quantity B

55


In how many ways can 5 identical apples be put into 3 different bowls such that at least 1 apple is included in each bowl?
Fred`s suitcase contains 4 shirts, 3 pair of pants, and 2 pair of shoes. A matching outfit consists of any shirts, any pair of pants, and any pair of shoes, except that one of the shirts does not match one of the pairs of pants. How many matching outfits can be selected from Fred`s suitcase?
One person has 5 shirts, 4 trousers and 3 shoes, of which one shirt and one trousers can not be combined. How many combinations are possible?
Four guests A, B, C and D have to be assigned into three different office rooms (one double room and two single rooms) such that A and B won`t have to stay in the double room at the same time. How many ways in total can they be assigned into these office rooms?
How many different 5-digit numbers can be formed by one "1",two "2",and two "3"?
The letters in a certain name can be arranged in exactly 180 different orders. Which of the following could be that name?
The vehicles of Company W are numbered consecutively from 1 to 650. The vehicles with a number that ends with one of the digits 1, 2, 3, 4, or 5 are used by Division 1. Vehicles with a number between 130 and 389, inclusive, are trucks. What percent of the company vehicles are trucks used by Division 1?
Three numbers are to be selected at random and without replacement from the five numbers 4, 5, 7, 8 and 11. What is the probability that the three numbers selected could be the lengths of the sides of a triangle?
What is the probability that the one 3-digit and one 2-digit integers that could be formed out of 1, 2, 3, 4 and 5 (each figure is used for only once) are both even integers?

Give your answer as a fraction.
When randomly selecting four different integers from 1 to 9, inclusive, the probability that 1, 2, 3 and 4 are selected in the above order is x, while the probability that 1,2 3 and 4 are selected no matter in what order is y. What is the ratio of x to y?

Give your answer as a fraction.
Event A and B are complementary events. The probability that event A occurs is p, while the probability that event B occurs is 2p

Quantity A

p

Quantity B

1-p


p is a value of probability greater than 0.5

Quantity A

2p

Quantity B

$$p^{2}$$


In a probability experiment, R, S, and T are events such that P(S)=P(T)=x, P(R)=kx, and P(R or S) < P(S or T), where k and x are positive numbers. Events R and S are mutually exclusive, and events S and T are independent.

Quantity A

k

Quantity B

1-x


Two containers, each with some white and black balls. Container T includes 20 white and 30 black balls. When selecting one ball out of each box, the possibility of getting 2 white balls is 0.3, what is the probability of getting black ball from U?

Give your answer as a decimal.
A bag contains 6 balls of which 2 are red and 4 are green. If 2 balls are to be chosen at random one after the other, without replacement. what is the probability that the second ball chosen will be red?
A bag contains 13 blue pens and 3 red pens. Two pens are to be randomly selected from the bag, one at a time and without replacement. What is the probability that both of the pens selected will be blue?

Give your answer as a decimal.


A box contains 12 candies of four different flavors. The table above shows the numbers of candies of each flavor. If 2 candies are to be selected at random from the box, without replacement, what is the probability that of the 2 candies selected one will be a caramel candy and the other will be a cherry candy?

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