In the triangle m∠1 = 42°, and m∠4 =81°. What is m∠2°?

Jeanne wants to start collecting coins and orders a coin collection starter kit. The kit comes with three coins chosen at random

lesya692 [45]

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

3 0

2 years ago

Quadrilateral ABCD is similiar to quadrilateral EFGH. The lengths of the three longest sides in quadrilateral ABCD are 24 feet,

masha68 [24]

Well the sides of these 2 quadrilaterals are proportional to each other , so you would have to find the scale factor of the 2 then see which sides have already proportional pairs , then multiply *or / to find the last one .

Answer: D. 11.7 ft

5 0

1 year ago

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Matias stepmother uses 30% off coupon to buy the ingredients for huevos rancheros she spends $28

fredd [130]

The original total of the ingredients was 40 dollars

8 0

2 years ago

Read 2 more answers

D2-9k+3 for d=10 and k=9

AVprozaik [17]

Answer:

22

Step-by-step explanation:

10^2-9(9)+3

100-81+3

19+3

22

8 0

1 year ago

Benito wrote the equations shown about the figure. Explain Benito’s errors.

Minchanka [31]

Answer:

Benito's error was using the equal sign (=) instead of the congruency symbol (≅).

Explanation:

Benito's error was using the equal sign (=) instead of the congruency symbol (≅).

The congruency symbol (≅) means that the elements (segments, angles or figures in general) have the same measure, i.e. they have equal lengths for the segments or equal measure for the angles.

For instance, it is an error saying that the segment AB is equal to the segment BC because, as you clearly see in the picture, they are not same; they have the same length but they are joining different points, that makes them different in essence, although they have the same length. They would be equal only if they are the same figure.

In mathematics, you must not say that two different segments or two different angles are equal but they are congruent, which means that their lengths are equal. The use of equal is reserved for numbers and variables, not for figures like segment, points, angles, polygons.

7 0

1 year ago