An urn contains 4 balls: 1 white, 1 green and 2 red. We draw 3 balls with replacement. Find the probability that we did not see all three colors. Use two different calculations, as specified by (a) and (b) below. (a) Define the event W = {white ball did not appear} and similarly for G and R. Use inclusion-exclusion. (b) Compute the probability by considering the complement of the event that we did not see all three colors.

An urn contains 4 balls: 1 white, 1 green and 2 red. We draw 3 balls with replacement. Find the probability that we did not see all three colors. Use two different calculations, as specified by (a) and (b) below. (a) Define the event W = {white ball did not appear} and similarly for G and R. Use inclusion-exclusion. (b) Compute the probability by considering the complement of the event that we did not see all three colors.

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

See similar textbooks

Similar questions

Suppose that E and F are two events and that P(E) = 0.5 and P(FIE) = 0.3. What is P(E and F)? P(E and F) = (Simplify your answer.)
An urn contains 15 balls marked LOSE and 3 balls marked WIN. Suppose that Chuck and Delilia take turns selecting one ball from the urn, without replacement, where Vhuck makes the first selection. The individual that draws the third WIN ball wins the game. It does not matter who selected the first two. Show that the probability Chuck wins the game on his third selection is equal to 1/136.
We are given that P(A | B) = 0.4 and P(A) = 0.3. Since P(A | B) ≠ P(A), the occurrence of event B changes the probability that event A will occur. This implies that A and B are ---Select--- not independent independent events.So, to determine P(A and B), we can apply the general multiplication rule for events. Recall that P(B) = 0.9. P(A and B) = P(B) · P(A | B)
Suppose that there is a white urn containing two white balls and three red balls and there is a red urn containing two white balls and four red balls. An experiment consists of selecting at random a ball from the white urn and then (without replacing the first ball) selecting at random a ball from the urn having the color of the first ball. Find the probability that the second ball is red.
Suppose that there is a white urn containing three white balls and one red ball and there is a red urn containing two white balls and four red balls. An experiment consists of selecting at random a ball from the white urn and then (without replacing the first ball) selecting at random a ball from the urn having the color of the first ball. Find the probability that the second ball is red.
I need the answer as soon as possible
Jay-Z has applied to both The School of Hard Knocks and The University of OG's. He thinks the probability that The School of Hard Knocks will admit him is 0.4, the probability that The University of OG's will admit him is 0.5, and the probability that both will admit him is 0.2. Creating a Venn Diagram is Helpful. What is the probability that Jay-Z gets into The School of Hard Knocks but not The University of OGʻs?
Let A and B be two events with P(A and Bc) = 1. Find P(B). Recall that Bc denotes the complement of the event B.
Urn 1 contains 4 red and 6 white balls. Urn 2 contains 3 red and 6white balls. A ball is drawn from urn 1 and placed in urn 2. Then a ball is drawn from urn 2. If the ball drawn from urn 2 is red, what is the probability that the ball drawn from urn 1 was red?
a and b
Suppose that there is a white urn containing two white balls and three red balls and there is a red urn containing one white ball and two red balls. An experiment consists of selecting at random a ball from the white urn and then (without replacing the first ball) selecting at random a ball from the urn having the color of the first ball. Find the probability that the second ball is red. The probability of the second ball being red is?