The probability of rain on a day of the year selected at random is 0.25 in a certain city. The local weather forecast is correct 60% of the time when the forecast is rain and 80% of the time for other forecasts. What is the probability that the forecast on a day selected at random is correct

0.75

Step-by-step explanation:

Let R be the event that it will rain, then R' will be the event that it will not rain

Let C be the event thatt forecast is correct.

Given: P(R)=0.25  P(R') =1-0.5=0.75

P(C|R)=0.60     P(C|R')=0.80

By law of total probability, we have

P(C)= P(C|R) × P(R) + P(C|R') ×P(R')

i.e. P(C) = 0.60×0.25+0.80×0.75

=0.75

Hence, the probability that the forecast on a day selected at random is correct = 0.75

1/4 because there is 4 grades.

the system of inequalities is

step-by-step explanation:

step 1

find the equation of the dashed line

we have the points

(0,0) and (3,1)

the line passes through the origin, so, is a direct variation

find the slope

the equation of the dashed line is

the solution of the inequality a s the shaded area above the dashed line

therefore

the equation of the inequality a is

step 2

find the equation of the solid line

we have the points

(4,0) and (0,4)

find the slope

the equation of the solid line is

the solution of the inequality b s the shaded area below the solid line

therefore

the equation of the inequality b is

step 3

the system of inequalities is