A producer wants to maximize its sale of special product which influen

Grady Turner

Grady Turner

Answered question

2021-11-17

A producer wants to maximize its sale of special product which influenced directly weather conditions. In this sense, it must predict temperature and wind. Lets

Answer & Explanation

kayleeveez7

kayleeveez7

Beginner2021-11-18Added 10 answers

Step 1
Note: " Since you have used multiple sub-parts, we will solve the first three sub-parts for you. If you want any specific question to be solved, then please specify the question number or post only that question.
- It was stated that a producer wants to maximize its sale of special product which influenced directly weather conditions.
- In this sense, it must predict temperature and wind.
- The event "warm day" is denoted as event A and the event "windy day" is denoted as event B.
- The weather forecast indicates that the probability of a windy day is 0.80.
- The probability of a warm day is 0.30.
- The probability of a warm and windy day is 0.28.
From the given data:
P(A)=0.30
P(B)=0.80
P(AB)=0.28
Need to find the following:
Step 2
a) Need to find if the two events A and B are independent.
If two events are independent then,
P(AB)=P(A)×P(B)
Lets us consider the right hand side,
Then,
P(A)×P(B)=0.30×0.80
=0.24
Since the P(AB)P(A)×P(B) the two events are not independent.
Step 3
b) Need to find the probability of the event "windy day will be warm".
The required conditional probability is given as,
P(AB)=P(AB)P(B)
=0.280.80
0.35
Thus, the the probability of the event "windy day will be warm" is 0.35.
Step 4
c) Need to find probability of the event "warm day will be windy".
The required conditional probability is given as,
P(BA)=P(AB)P(A)
=0.280.30
0.934
Thus, the probability that "warm day will be windy" is 0.934.

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