Multiplication Rule of Probability: Dependent EventsIf events A and B are dependent events such that the outcome of A affects theoutcome of B, then the probability that "event A followed by event B" happens isP(AB) = P(A) xP(B|A)where P(A) is the probability that event A happens and P(BA) is the probability thatevent B happens after A happened.1. Josiah draws 2 cards at random from a standard deck of 52 cars without replacement. What is the probabilityof getting 2 ace cards?2. Gabriel has a candy box containing 9 chocolate candies and 12 lollipops. If he chooses 2 of them at random,what is the probability that he gets 2 lollipops?

Answered: Multiplication Rule of Probability:…

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...

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Whenever Suzan sees a bag of marbles, she grabs a handful at random. she has seen a bag containing 3 red marbles, two green ones, 4 white ones, and 1 purple one. she grabs 8 of them. find the probability of the following event , expressing it as fraction in the lowest term. she has all the red ones ______________
Events A and B are independent. Find the missing probability. P(A) = (1/2), P(A and B) = (5/6), P(B) = 3/5 1/2 1/4 4/5
Recall from Example 1 that wherever Suzan sees a bag of marbles, she grabs a handful at random. She has seen a bag containing four red marbles, two green ones, four white ones, and two purple ones. She grabs seven of them. Find the probability of the following event, expressing it as a fraction in lowest terms. HINT (See Example 1.) She has at most one green one.
If two events, A & B, are mutually exclusive, then the probability that either event would happen is? * P(A) + P(B) – P(A & B) always equal to 0 always equal to 1 O P(A) + P(B)
Show all workings - use formulas: A group consists of 10 girls and 8 boys. A team of 9 are to be selected from this group. What is the probability that the team selected will consist of 5 girlsand 4 boys, but will not include ANY of 4 specific boys?
Events A and B are independent events with P(A) = 0.25 and P(B) = 0.35. The probability of the complement of Event B equals
EC2
Let A and B be two events such that the probability of B is 0.5 and the probability of both is 0.2. Find the probability of A given that B occurs.
Suppose events B and C are independent and P(B) = - 1 P(C) = 12 4 Find the probability. (Enter the probability as a fraction.) P(BUC)
A conditional Probability: P(A | B) is asking what is the probability we get event A if we know that event B occurred. A useful formula: P (A | B) = ||| P(A and B) P(B) Or: P(A | B) = (remaining # of ways to get A) / (remaining number of possible outcomes) A bag has 5 red balls, 7 green balls, and 8 purple balls. Two balls are going to be selected. After the first ball is drawn it is NOT returned to the bag. Find the probability the second is a red ball if you know the first chosen is a red ball. If A = event a red ball is selected: P(A|A) = ?
Suppose that events A and B are mutually exclusive with P(A) = 1 2 and P(B) = 1 6 . (Enter your answers as fractions.) (a) Are A and B independent events? Explain how you know. Since the events are mutually exclusive we know P(A|B) = which P(A) and thus the events are . (b) Are A and B complementary events? Explain how you know. We know that P(A) + P(B) = . And, since P(A) + P(B) 1, the events A and B complementary events.

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