Question 1
Two dice are thrown. One die is biased so that the probabilities of throwing the six numbers are all different. The other die is unbiased. Calculate the probability that the numbers shown on the two dice are the same.
Question 2
A bag contains 8 black balls and 1 white ball. A second bag contains 7 black balls. Four balls are taken at random from the first bag and placed in the second bag. Find the probability that the white ball is now
(a) in the first bag
(b) in the second bag
Question 3
Show that the probability that a point, selected at random inside a circle, is closer to the centre of the circle then to the circumference is 1/4.
Thank you for your kind attention.
Regards,
ahm97sic
22 percent!
Originally posted by Ahm97sic:
Question 1
Two dice are thrown. One die is biased so that the probabilities of throwing the six numbers are all different. The other dice is unbiased. Calculate the probability that the numbers shown on the two dice are the same.
Question 2
A bag contains 8 black balls and 1 white ball. A second bag contains 7 black balls. Four balls are taken at random from the first bag and placed in the second bag. Find the probability that the white ball is now
(a) in the first bag
(b) in the second bag
Question 3
Show that the probability that a point, selected at random inside a circle, is closer to the centre of the circle then to the circumference is 1/4.
Thank you for your kind attention.
Regards,
ahm97sic
first, dice or die?
1) total probability = both dice 1 + both dice 2 + both dice 3...
=a x 1/6 + b x 1/6 +.....
= a/6 + b/6 + c/6 ....
= (a+b+c+...)/6
= 1/6
where a, b, c is the probability for each die.
2) 4/9 chance the white ball is chosen.
a) 5/9
b) 4/9
3) area of circle = pi x r^2
area of circle closer to center = pi X (r/2) ^2
= pi x r^2/4
hence, 1/4
thanks for the fun questions!