Mathematics, 29.10.2019 01:31 LucidDreamer16

Jeanne wants to start collecting coins and orders a coin collection starter kit. the kit comes with three coins chosen at random, each in a small envelope. each coin is either a nickel, a dime, or a quarter. use conditional probability to solve the following:

what is the probability that all three coins are quarters if the first two envelopes jeanne opens each contain a quarter?
what is the probability that all three coins are different if the first envelope jeanne opens contains a dime?

Answers: 1

Show answers

Answers

Conditional probability is a measure of the probability of an event given that another event has occurred. If the event of interest is A and the event B is known or assumed to have occurred, "the conditional probability of A given B", or "the probability of A under the condition B", is usually written as P(A|B), or sometimes P_B(A)

.

The conditional probability of event A happening, given that event B has happened, written as P(A|B) is given by
$P(A|B)= \frac{P(A \cap B)}{P(B)}$

In the question, we were told that there are three randomly selected coins which can be a nickel, a dime or a quarter.

The probability of selecting one coin is $\frac{1}{3}$

Part A:
To find the probability that all three coins are quarters if the first two envelopes Jeanne opens each contain a quarter, let the event that all three coins are quarters be A and the event that the first two envelopes Jeanne opens each contain a quarter be B.

P(A) means that the first envelope contains a quarter AND the second envelope contains a quarter AND the third envelope contains a quarter.

Thus $P(A)= \frac{1}{3} \times \frac{1}{3} \times \frac{1}{3} = \frac{1}{27}$

P(B) means that the first envelope contains a quarter AND the second envelope contains a quarter

Thus $P(B)= \frac{1}{3} \times \frac{1}{3} = \frac{1}{9}$

Therefore, $P(A|B)=\left( \frac{ \frac{1}{27} }{ \frac{1}{9} } \right)= \frac{1}{3}$

Part B:
To find the probability that all three coins are different if the first envelope Jeanne opens contains a dime, let the event that all three coins are different be C and the event that the first envelope Jeanne opens contains a dime be D.

$P(C)= \frac{3}{3} \times \frac{2}{3} \times \frac{1}{3} = \frac{6}{27} = \frac{2}{9}$

$P(D)= \frac{1}{3}$

Therefore, $P(C|D)=\left( \frac{ \frac{2}{9} }{ \frac{1}{3} } \right)= \frac{2}{3}$

Answer from: Quest

answer: -1

step-by-step explanation:

Answer from: Quest

you forgot the options, but i found them anyways, the correct answer is "john wilson believes that words and actions based on the intellect are superior to those based on emotions".

john wilson is depicted as an extremely intelligent man. the point of the excerpt is to make a sort of distinction between emotional and rational intelligence. he happens to have both attributes, but he clearly favors his intellectual gifts. at the same time, because of his religious background, he's a little bit conflicted with this and it makes him ashamed.

hope this !

Another question on Mathematics

Mathematics, 21.06.2019 14:30

Cass decided to sell game programs for the hockey game. the printing cost was over 20 cents per program with a selling price of 50 cents each. cass sold all but 50 of the programs, and made a profit of $65. how many programs were printed? letting p represent the number of programs printed, set up an equation that describes this situation. then solve your equation for p.

Answers: 1

Answer

Mathematics, 21.06.2019 16:00

Areal estate agent earns $32,000 a year plus $1,000 for each apartment he sells. write an equation that shows the relationship between the number of apartments abe sells,n, and the total amount he earns in a year,e. what is the total amount abe would earn from selling 10 apartments in one year

Answers: 3

Answer

Mathematics, 21.06.2019 18:30

Atriangle with all sides of equal length is a/an triangle. a. right b. scalene c. equilateral d. isosceles

Answers: 2

Answer

Mathematics, 21.06.2019 20:00

Afrequency table of grades has five classes (a, b, c, d, f) with frequencies of 3, 13, 14, 5, and 3 respectively. using percentages, what are the relative frequencies of the five classes?

Answers: 3

Answer

You know the right answer?

Jeanne wants to start collecting coins and orders a coin collection starter kit. the kit comes with...

Questions

Mathematics, 22.05.2020 03:00

Eriko cuts out a paper quadrilateral with two angles that each measure 60° and two angles that each measure 120°. Only two of the sides have a length...

Mathematics, 22.05.2020 03:00

Can anyone help with this lol-? The figure shown is composed of two regular pentagons. What is the area of the shaded region? A.