Probability

1003019101

Level:

An urn contains chips with the numbers from

1

30

. What is the probability that the chip with a prime number is drawn?

\frac{1}{3} ≐ 0.3333

\frac{11}{30} ≐ 0.3667

\frac{2}{5} = 0.4

\frac{3}{10} = 0.3

1003019102

Level:

An urn contains

19

red balls and

9

blue balls. Find the least number of blue balls that need to be added to the urn to ensure higher probability of drawing a blue ball than

0.65

27

26

10

0

1003019103

Level:

There are

30

students in the class, one of them is Adam. The teacher picks randomly three students to be tested. What is the probability that Adam is among them?

\frac{(\binom{29}{2})}{(\binom{30}{3})} = 0.1

\frac{(\binom{29}{2})}{(\binom{30}{2})} ≐ 0.9333

\frac{(\binom{29}{3})}{(\binom{30}{3})} = 0.9

\frac{(\binom{3}{1}) (\binom{27}{2})}{(\binom{30}{3})} ≐ 0.2594

1003019104

Level:

Four dice are thrown. What is the probability that the sum is

6

\frac{10}{6^{4}} ≐ 0.0077

\frac{1}{21} ≐ 0.0476

\frac{1}{6^{4}} ≐ 0.0008

\frac{2}{6^{4}} ≐ 0.0015

1003029201

Level:

Three dice are thrown together. Let

A

be the event “the sum is

5

” and

B

be the event “the sum is

16

”. Which of the following statements is true?

Events

A

and

B

have the same probability of occurrence.

Event

A

is more likely to occur than event

B

Event

B

is more likely to occur than event

A

1003029202

Level:

In a set of

100

items,

15

are defective. We pick randomly

10

items from this set. First eight items were not defective. Find the probability that the ninth item selected is not defective too. Results are rounded to two decimal places.

\frac{77}{92} = 0.84

\frac{85}{92} = 0.92

\frac{15}{92} = 0.16

\frac{7}{92} = 0.08

1003041601

Level:

The wooden cube with the edges of length

5 cm

has faces painted in blue. Suppose we cut the cube into small unit cubes (the edge length is

1 cm

) and select one of the unit cubes at random. What is the probability that the selected cube has at least two faces painted in blue?

0.352

0.288

0.480

0.432

1003041701

Level:

Find the probability that a two-digit number selected at random is even or a power of

2

\frac{45}{90} = 0.5

\frac{48}{90} ≐ 0.5333

\frac{42}{90} ≐ 0.4667

\frac{45}{90} \cdot \frac{3}{90} ≐ 0.1667

2000003401

Level:

One dice is thrown. What is the probability of getting a number divisible by three?

\frac{1}{3}

\frac{1}{6}

\frac{1}{2}

\frac{2}{3}

2000003402

Level:

Two dice are thrown. What is the probability of the total number being a two-digit prime number?

\frac{2}{36} = \frac{1}{18}

\frac{11}{36}

\frac{1}{36}

\frac{3}{36} = \frac{1}{12}

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