Probability

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Level:

Two dices are rolled. Find the probability that we get either the same number on both dices or the sum of the numbers on both dices is

6

\frac{10}{36} ≐ 0.2778

\frac{11}{36} ≐ 0.3056

\frac{6}{36} ≐ 0.1667

\frac{5}{36} ≐ 0.1389

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Level:

The probability that Robin Hood hits the target is

0.83

. The same probability is

0.61

for Robin's fellow, Little John. Both Robin and John shot on the wolf. Find the probability that they will hit the wolf. Round your answer to three decimal places.

0.934

1.440

0.506

0.494

A man plays a dice game. He rolls one dice three times and to win he needs at least one number six. However, the dice is not fair. The probability of an even number is two times bigger than the probability of an odd number. Find the probability that the man wins. Suppose that all even numbers have equal probability and all odd numbers also have equal probability. Round your answer to three decimal places.

0.529

0.471

0.421

0.579

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Level:

The Robin's band has

10

men and

5

women. From this group they select randomly two fellows to negotiate with the Sheriff of Nottingham. Find the probability that there will be one man and one woman in the selected pair. Round your answer to three decimal places.

0.476

0.952

0.325

0.675

1003019205

Level:

Adam and Eve met at the disco. They agreed to meet the next day at the same location sometime between

1

p.m. and

2

p.m. Both of them will arrive independently at random times within the hour and wait ten minutes for the other. What is the probability that they will not meet during that hour?

\frac{25}{36} ≐ 0.6944

\frac{11}{36} ≐ 0.3056

\frac{35}{36} ≐ 0.9722

\frac{24}{36} ≐ 0.6667

1003029203

Level:

Three dice are thrown together. Find the probability that three different outcomes are rolled. Results are rounded to two decimal places.

\frac{(\binom{6}{1}) \cdot (\binom{5}{1}) \cdot (\binom{4}{1})}{6^{3}} = 0.56

\frac{(\binom{6}{1}) + (\binom{5}{1}) + (\binom{4}{1})}{6^{3}} = 0.07

\frac{(\binom{6}{6}) \cdot (\binom{6}{5}) \cdot (\binom{6}{4})}{6^{3}} = 0.42

\frac{(\binom{6}{6}) + (\binom{6}{5}) + (\binom{6}{4})}{6^{3}} = 0.10

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Level:

A class consists of

50

students including twins, Mark and Martin. For an exam students are randomly divided into two equally sized subgroups. Find the probability that Mark and Martin will be in the same subgroup. The results are rounded to two decimal places.

\frac{(\binom{48}{23}) + (\binom{48}{25})}{(\binom{50}{25})} = 0.49

\frac{(\binom{48}{23})}{(\binom{50}{25})} = 0.24

\frac{2 \cdot (\binom{48}{24})}{(\binom{50}{25})} = 0.51

\frac{(\binom{49}{24})}{(\binom{50}{25})} = 0.50

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Level:

In the hospital,

22

boys and

18

girls were born in one month. Babies were listed in the register by their date of birth. Find the probability that there are two boys and three girls in the first five places of the register. The results are rounded to four decimal places.

\frac{(\binom{22}{2}) \cdot (\binom{18}{3})}{(\binom{40}{5})} = 0.2865

\frac{(\binom{22}{2}) \cdot (\binom{18}{3})}{\frac{40!}{35!}} = 0.0024

\frac{22^{2} \cdot 18^{3}}{40^{5}} = 0.0276

\frac{(\binom{22}{3}) \cdot (\binom{18}{2})}{\frac{40!}{35!}} = 0.0030

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Level:

In the hospital,

22

boys and

18

girls were born in one month. Babies were listed in the register by their date of birth. Find the probability that there are at least three boys in the first five places of the register. The results are rounded to four decimal places.

\frac{(\binom{22}{3}) \cdot (\binom{18}{2}) + (\binom{22}{4}) \cdot (\binom{18}{1}) + (\binom{22}{5}) \cdot (\binom{18}{0})}{(\binom{40}{5})} = 0.5982

\frac{(\binom{22}{3}) + (\binom{22}{4}) + (\binom{22}{5})}{(\binom{40}{5})} = 0.0535

\frac{22^{3} \cdot 18^{2} + 22^{4} \cdot 18^{1} + 22^{5} \cdot 18^{0}}{40^{5}} = 0.1252

\frac{(\binom{22}{3}) \cdot (\binom{18}{2}) + (\binom{22}{4}) \cdot (\binom{18}{1}) + (\binom{22}{5}) \cdot (\binom{18}{0})}{40^{5}} = 0.0038

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Level:

The probability of a man hitting a target is

0.9

. If the man shoots three times, what is the probability that he hits the target at least once? Round the result to three decimal places.

0.999

0.729

0.027

0.243

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