# Several probability problems and their solutions

#### romsek

Math Team
New questions from Whois.

Problem 6

10 distinguishable dice are thrown. What's the probability that an equal number of "ones" and "sixes" come up?

Problem 7

3 distinguishable even dice are thrown. What's the probability of the event A = {the sum and the product of the numbers that come up are equal}?

Problem 8

From an urn, which contains 10 white, 7 green and 6 red balls, 1 ball is taken out. What's the probability that the ball, which was taken out is:
a) white
b) green
c) red

Problem 9

An urn contains 8 white and 4 black balls. Two balls are simultaneously taken out. What is more probable: that the two balls are white or that the two
balls are with a different color?

Problem 10

From an urn, which contains 12 white and 8 black balls, 2 balls are simultaneously taken out. Find the probability of the events:
A={both balls are white}
B={both balls are black}
c={the two balls have different colors}

Problem 11

From an urn, which contains M white and N black balls, 2 balls are simultaneously taken out. Find the probability of the events:
A={both balls are white}
B={both balls are black}
C={the two balls have different colors}

Problem 12

In an urn there are 2*M white and 2*N black balls. M+N balls are simultaneously subtracted. What's the probability that M white and N black balls remain
in the urn?