2000017509
Level:
A
The probability of getting \(4\) heads in \(4\) tosses of a coin is:
\(\frac1{16}\)
\(\frac1{12}\)
\(\frac1{10}\)
\(\frac1{8}\)
A
2000017508
Level:
A
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:
A
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:
A
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 \(3\)?
\(\frac16\)
\(0\)
\(1\)
\(\frac14\)
2000017505
Level:
A
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:
A
The probability of a student completing a medical degree is \(0.3\). What is the probability that at least \(2\) of \(7\) students finish the university successfully? Round your result to \(2\) decimal places.
\(0.67\)
\(0.05\)
\(0.85\)
\(0.50\)
2000017503
Level:
A
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:
A
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.
\(\frac13\)
\(\frac14\)
\(\frac15\)
\(\frac18\)
2000017501
Level:
A
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:
A
Find \(\frac{K \cdot (-L)}2\), if:
\[
K=\left (\array{
3& 0 & 1\cr
2 & 3 & 4 \cr
1& -1 & 1} \right ),~
L=\left (\array{
2& 3 & 0\cr
1 & 1 & -1 \cr
2 &0& 1 } \right )
\]
\(
\left (\array{
-4& -4.5 & -0.5\cr
-7.5 & -4.5& -0.5\cr
-1.5 & -1& -1 } \right )
\)
\(
\left (\array{
-4& 4.5 & 0.5\cr
-7.5 & -4.5& -0.5\cr
-1.5 & -1& -1 } \right )
\)
\(
\left (\array{
-4& -4.5 & -0.5\cr
7.5 & -4.5& -0.5\cr
-1.5 & -1& -1 } \right )
\)
\(
\left (\array{
-4& -4.5 & -0.5\cr
-7.5 & 4.5& -0.5\cr
-1.5 & -1& 1 } \right )
\)