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Sergio039 [100]
3 years ago
6

How do i write proofs like this?

Mathematics
1 answer:
kirill115 [55]3 years ago
7 0
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Suppose that Kevin can choose to get home from work by car or bus. When he chooses to get home by car, he arrives home after 7 p
astraxan [27]

Answer:

The approximate probability that Kevin chose to get home from work by bus, given that he arrived home after 7 pm = 0.838

Step-by-step explanation:

Let the probability that Kevin arrives home after 7 pm be P(L)

Probability that Kevin uses the bus = P(B)

Probability that Kevin uses the car = P(C)

Probability of arriving home after 7 pm if the car was taken = P(L|C) = 4% = 0.04

Probability of arriving home after 7 pm if the bus was taken = P(L|B) = 15% = 0.15

The bus is cheaper, So, he uses the bus 58% of the time.

P(B) = 58% = 0.58

P(C) = P(B') = 1 - P(B) = 1 - 0.58 = 0.42

The approximate probability that Kevin chose to get home from work by bus, given that he arrived home after 7 pm = P(B|L)

The conditional probability P(A|B) is given mathematically as

P(A|B) = P(A n B) ÷ P(B)

Hence, the required probability, P(B|L) is given as

P(B|L) = P(B n L) ÷ P(L)

But we do not have any of P(B n L) and P(L)

Although, we can obtain these probabilities from the already given probabilities

P(L|C) = 0.04

P(L|B) = 0.15

P(B) = 0.58

P(C) = 0.42

P(L|C) = P(L n C) ÷ P(C)

P(L n C) = P(L|C) × P(C) = 0.04 × 0.42 = 0.0168

P(L|B) = P(L n B) ÷ P(B)

P(L n B) = P(L|B) × P(B) = 0.15 × 0.58 = 0.087

P(L) = P(L n C) + P(L n B) = 0.0168 + 0.087 = 0.1038 (Since the bus and the car are the two only options)

The approximate probability that Kevin chose to get home from work by bus, given that he arrived home after 7 pm

= P(B|L) = P(B n L) ÷ P(L)

P(B n L) = P(L n B) = 0.087

P(L) = 0.1038

P(B|L) = (0.087/0.1038) = 0.838150289 = 0.838

Hope this Helps!!!

8 0
3 years ago
Identify which type of sampling is​ used: random,​ systematic, convenience,​ stratified, or cluster. To determine customer opini
azamat

Answer:

This is cluster sampling.

Step-by-step explanation:

American Airlines randomly selects 110 flights during a certain week and surveys all passengers on the flights.

This is a type of cluster sampling.

This type of sampling is done by dividing the population into different groups and a simple random sample of clusters is selected from the population.

8 0
3 years ago
Number of real solutions?<br><br> 8x^2 - 11x = -3<br><br> -4x^2 - 4 = 8x
Anna71 [15]

(1) ANSWER

x =  \frac{3}{8}  \: or \:  x = 1

(2) ANSWER

x =  - 1

3 0
3 years ago
What is the value of x + y(3 - x) when x = -5 and y = 3?
cestrela7 [59]

Answer:

E. 19

Step-by-step explanation:

Step 1: Plug in the x and y values mentioned:

-5 + 3(3 - (-5))=

Step 2: Distribute the three:

-5 + 9+15=

Simplify:

19

<em>Hope this helped and plz mark as brainliest!</em>

<em></em>

<em>Luna G.</em>

4 0
3 years ago
Every radius of a circle is a chord
Ugo [173]
False

A chord touches the  circle at 2 points.
5 0
3 years ago
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