Two people toss a coin: one tosses it 10 times, the other – 11 times. What is the probability that the second person’s coin showed heads more times than the first?
There are 30 students in the class. Prove that the probability that some two students have the same birthday is more than 50%.
The frog jumps over the vertices of the hexagon
a) How many ways can it get from
b) The same question, but on condition that it cannot jump to
c) Let the frog’s path begin at the vertex
d)* What is the average life expectancy of such frogs?
Carry out the following experiment 10 times: first, toss a coin 10 times in a row and record the number of heads, then toss the coin 9 times in a row and again, record the number of heads. We call the experiment successful, if, in the first case, the number of heads is greater than in the second case. After conducting a series of 10 such experiments, record the number of successful and unsuccessful experiments. Collect the statistics in the form of a table.
a) Anton throws a coin 3 times, and Tina throws it two times. What is the probability that Anton gets more heads than Tina?
b) Anton throws a coin
Is it possible to:
a) load two coins so that the probability of “heads” and “tails” were different, and the probability of getting any of the combinations “tails, tails,” “heads, tails”, “heads, heads” be the same?
b) load two dice so that the probability of getting any amount from 2 to 12 would be the same?
On a roulette, any number from 0 to 2007 can be determined with the same probability. The roulette is spun time after time. Let
The figure shows the scheme of a go-karting route. The start and finish are at point
It takes Fred one minute to get from
On the occasion of the beginning of the winter holidays all of the boys from class 8B went to the shooting range. It is known that there are
a) Find the average number of affected targets.
b) Can the average number of affected targets be less than
An exam is made up of three trigonometry problems, two algebra problems and five geometry problems. Martin is able to solves trigonometry problems with probability
a) With what probability does Martin solve at least five problems?
Martin decided to work hard on the problems of any one section. Over a week, he can increase the probability of solving the problems of this section by 0.2.
b) What section should Martin complete, so that the probability of solving at least five problems becomes the greatest?
c) Which section should Martin deal with, so that the mathematical expectation of the number of solved problems becomes the greatest?
What is the mathematical expectation of the number of people that can be seen?