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2000017508

Level:

We have a pack with

54

cards. There are exactly four aces inside. We choose two cards from the package in a random manner without putting back. What is the probability that we choose two aces? Round your answer to

4

decimal places.

0.0042

0.0370

0.0002

0.9958

2000017507

Level:

Two dice are rolled together. Let

A

be the event “the product is

4

” and

B

be the event “the product is

6

”. Which of the following statements is true?

Event

B

is more likely to occur than event

A

Event

A

is more likely to occur than event

B

Events

A

and

B

have the same probability of occurrence.

2000017506

Level:

We have randomly rolled the standard dice for

7

times. The result was always number

3

. What is the probability that the next result will also be number

3

\frac{1}{6}

0

1

\frac{1}{4}

2000017505

Level:

A family has

4

children. What is the probability that

3

of them are girls? Suppose that the probability of giving birth to a boy and a girl in the family is the same.

0.25

0.4

0.75

0.89

2000017504

Level:

The probability of a student completing a medical degree is

0.3

. What is the probability that at least

2

7

students finish the university successfully? Round your result to

2

decimal places.

0.67

0.05

0.85

0.50

2000017503

Level:

An exam consists of

10

dual-choice questions, true / false. What is the probability that I will accidentally guess exactly

6

of them? Round your result to

3

decimal places.

0.205

0.015

0.490

0.125

2000017502

Level:

María has two children, at least one of them is a girl. What is the probability that they are both girls? Suppose that the probability of giving birth to a boy and a girl is the same.

\frac{1}{3}

\frac{1}{4}

\frac{1}{5}

\frac{1}{8}

2000017501

Level:

Assume that a year consists of

365

days. If

50

people gather at the party, what is the probability that at least

2

of them will celebrate the birthday on the same day? Round your result to

2

decimal places.

0.97

0.26

0.73

0.18

2000017408

Level:

Find

\frac{K \cdot (- L)}{2}

, if:

K = (\begin{matrix} 3 & 0 & 1 \\ 2 & 3 & 4 \\ 1 & - 1 & 1 \end{matrix}), L = (\begin{matrix} 2 & 3 & 0 \\ 1 & 1 & - 1 \\ 2 & 0 & 1 \end{matrix})

(\begin{matrix} - 4 & - 4.5 & - 0.5 \\ - 7.5 & - 4.5 & - 0.5 \\ - 1.5 & - 1 & - 1 \end{matrix})

(\begin{matrix} - 4 & 4.5 & 0.5 \\ - 7.5 & - 4.5 & - 0.5 \\ - 1.5 & - 1 & - 1 \end{matrix})

(\begin{matrix} - 4 & - 4.5 & - 0.5 \\ 7.5 & - 4.5 & - 0.5 \\ - 1.5 & - 1 & - 1 \end{matrix})

(\begin{matrix} - 4 & - 4.5 & - 0.5 \\ - 7.5 & 4.5 & - 0.5 \\ - 1.5 & - 1 & 1 \end{matrix})

2000017409

Level:

Let

A = (\begin{matrix} 1 & 2 \\ a & 1 \end{matrix}), B = (\begin{matrix} 7 & 4 \\ 6 & 7 \end{matrix}),

where

a

is a real number. For which

a

the equality

A \cdot B = B \cdot A

holds?

3

- 3

3.5

- 3.5

A

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