Question
Suppose there is an urn with 6 red balls and 4 yellow balls. We draw two balls from the urn, without replacement. (a) What is the probability that both balls are red? (b) What is the probability that both balls are yellow? (c) What is the probability of drawing one red and one yellow ball, in either order? (d) What is the probability that at least one of the balls is yellow?
235
likes1173 views
Answer to a math question Suppose there is an urn with 6 red balls and 4 yellow balls. We draw two balls from the urn, without replacement. (a) What is the probability that both balls are red? (b) What is the probability that both balls are yellow? (c) What is the probability of drawing one red and one yellow ball, in either order? (d) What is the probability that at least one of the balls is yellow?
Hester
4.8117 Answers
a) the probability that both balls are red = \frac{6}{6+4}\cdot\frac{\left(6-1\right)}{6+4-1}\:=\:\frac{6}{10}\cdot\frac{5}{9}\:=\:\:\frac{1}{3}
b) the probability that both balls are yellow = \frac{4}{6+4}\cdot\frac{\left(4-1\right)}{6+4-1}\:=\:\frac{4}{10}\cdot\frac{3}{9}\:=\:\:\frac{2}{15}
c) the probability of drawing one red and one yellow ball, in either order= \frac{6}{6+4}\cdot\frac{\left(4\right)}{6+4-1}\:=\:\frac{6}{10}\cdot\frac{4}{9}\:=\:\:\frac{4}{15}
d) the probability that at least one of the balls is yellow:
P\left(atleast\:1\:ball\:yellow\right)\:=\:1-\:P\left(atleat\:1\:ball\:yellow\right)\~\:=\:1-\:P\left(no\:ball\:is\:Yellow\right)
1-\:P\left(no\:Ball\:are\:yellow\right)\:=\:1-\:P\left(all\:are\:red\right)\:=\:1-\:\frac{1}{3}\:=\:\frac{2}{3}
Frequently asked questions (FAQs)
What is the length of the median of a triangle if the lengths of the other two medians are 5cm and 8cm?
+
What is 0.525 as a percent?
+
Find the vertex (h, k) of the parabola function 𝑦 = 3𝑥² + 2𝑥 - 1. [
+
New questions in Mathematics