The route used by a certain motorist in commuting to work contains two intersections with traffic signals. The probability that he must stop at the first signal is 0.45, the analogous probability for the second signal is 0.5, and the probability that he must stop at at least one of the two signals is 0.9.Required:
a. What is the probability that he must stop at both signals?
b. What is the probability that he must stop at the first signal but not at the second one?
c. What is the probability that he must stop at exactly one signal?
Answers
Answer: a. 0.05
b. 0.40
c. 0.85
Step-by-step explanation:
Let F= Event that a certain motorist must stop at the first signal.
S = Event that a certain motorist must stop at the second signal.
As per given,
P(F) = 0.45 , P(S) = 0.5 and P(F or S) = 0.9
a. Using general probability formula:
P(F and S) =P(F) + P(S)- P(F or S)
= 0.45+0.5-0.9
= 0.05
∴ the probability that he must stop at both signals = 0.05
b. Required probability = P(F but (not s)) = P(F) - P(F and S)
= 0.45-0.05= 0.40
∴ the probability that he must stop at the first signal but not at the second one =0.40
c. Required probability = P(exactly one)= P(F or S) - P(F and S)
= 0.9-0.05
= 0.85
∴ the probability that he must stop at exactly one signal = 0.85
Final answer:
The probability of stopping at both signals is 0.225, the probability of stopping at the first one but not the second one is 0.225. The probability of stopping at exactly one signal is 0.675.
Explanation:
The probability theory can be used to answer these questions. The probabilities of stopping at various traffic signals can be calculated using some assumptions about the independence of the events.
- The probability of the motorist having to stop at both signals can be found by multiplying the individual probabilities, assuming that these are independent events. So, P(stop at both signals) = P(stop at first signal) * P(stop at second signal) = 0.45 * 0.5 = 0.225.
- The probability of him stopping at the first signal but not at the second one is again found by multiplying the probability of stopping at the first by the probability of not having to stop at the second. Therefore, P(stop at first, not at second) = 0.45 * (1 - 0.5) = 0.225.
- To find the probability that the driver must stop at exactly one signal, we can subtract the probability of stopping at both signals from the probability of stopping at least one signal. So, P(stop at one signal) = P(stop at at least one signal) - P(stop at both signals) = 0.9 - 0.225 = 0.675.
Learn more about Probability here:
#SPJ3
Related Questions
If the probability that a bird will lay an egg is 75%, the probability that the egg will hatch is 50%, and the probability that the chick will be eaten by a snake before it fledges is 20%, what is the probability that a parent will have progeny that survive to adulthood?(A) 30%(B) 14.5%(C) 7.5%(D) 2%
Use implicit differentiation to find an equation of the tangent line to the curve at the given point. y 2 ( y 2 − 4 ) = x 2 ( x 2 − 5 ) , ( 0 , − 2 ) (devil's curve) y2(y2-4)=x2(x2-5), (0,-2) (devil's curve)
Hi I need help with the one that is circle thank you
Find a solution to the following initial-value problem: dy dx = y(y − 2)e x , y (0) = 1.
YZ measures units.
ZX measures units.
XYZ is a right triangle.
XYZ is a scalene triangle.
Answers
First, second and fourth options are true about triangle XYZ.
XY measures units.
YZ measures units.
ZX measures units.
XYZ is a right triangle.
What is right triangle?
A triangle in which one of the interior angles is 90° is called a right triangle. The longest side of the right triangle, which is also the side opposite the right angle, is the hypotenuse and the two arms of the right angle are the height and the base.
Given X (-1, 5), Y (4, 4), Z (-2, 0)
Distance between two points D =
|XY| =
|YZ| =
|XZ| =
So, XYZ is a right triangle.
So, the first, second and fourth options are correct.
Find out more information about right triangle here
#SPJ3
Answer: a and d
Step-by-step explanation:
edge
Answers
Answer:
A. 20 B. 25
Step-by-step explanation:
A. Perimeter equals the all the side lengths added together, so 5+5+5+5=20
B. Area equals (for a square) two side lengths multiplied by one another, so 5x5=25
Answers
Answers
Answer:
14.6
Step-by-step explanation:
The computation of average price paid for the share is shown below:-
=
= 14.6
For more clarification please find the attachment as attached using excel spreadsheet.
By dividing the total investment by the total number of shares we can get the average price paid for the share and the same is to be considered
Moreover, the total investment and the total shares are shown in the attachment. Kindly find it below:
Answers
Answer:To find out how long it will take for the two trains to meet, you can use the concept of relative speed. When two objects are moving toward each other, their relative speed is the sum of their individual speeds.
In this case, one train is traveling at 85 miles per hour, and the other is traveling at 95 miles per hour. So, their relative speed is:
Relative Speed = 85 mph + 95 mph = 180 mph
Now that you know the relative speed of the two trains, you can use the formula:
Time = Distance / Speed
The distance they need to cover to meet is 288 miles, and their relative speed is 180 mph. Plug these values into the formula:
Time = 288 miles / 180 mph
Time = 1.6 hours
So, it will take 1.6 hours for the two trains to meet. To express this in minutes, you can multiply by 60:
1.6 hours * 60 minutes/hour = 96 minutes
Therefore, it will take 96 minutes for the two trains to meet.
Step-by-step explanation:
6 in, 10 in, 18 in
10 in, 12 in, 15 in
10 in, 15 in, 6 in
10 in, 18 in, 12 in
Answers
In short, Your Answer would be Option A
Hope this helps!
The sides need to be in between (10-6) and (10+6) or between 4 and 16. But the third side here is 18, so that cannot qualify as a side.
Hope this helps.