1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
den301095 [7]
3 years ago
15

The route used by a certain motorist in commuting to workcontains two intersections with traffic signals. The probabilitythat he

must stop at the first signal is .4, the analogousprobability for the second signal is .5, and the probability thathe must stop at least one of the two signals is .6. What is theprobability that he must stop.
a.) At both signals?

b.) At the first signal but not at the second one?

c.) At exactly on signal?

Mathematics
2 answers:
Masja [62]3 years ago
8 0

Answer:

a) 0.3

b) 0.1

c) 0.3

Step-by-step explanation:

Lets call:

a = stop at first signal,  b = stop at second signal

The data we are given is P(a) = 0.4, and P(b)=0.5

Stoping at least at one is the event (a or b) = a ∪ b

P(a U b) = 0.6 is the other data we are given

a) Stoping at both signals is the event (a and b = a ∩ b)

The laws of probability say that:

P(a ∪ b)= P(a) + P(b) - P( a ∩ b) = 0.4 + 0.5  - P( a ∩ b) = 0.6

Then we get P( a ∩ b) = 0.3

b) The event is (a and not b) = a ∩(¬b).

P( a ∩(¬b) ) = P(a) - P( a ∩ b) = 0.1

c) The event is (a or b) without the cases in which (a and b)

P(a ∪ b) - P( a ∩ b) = 0.3

The Venn diagram can help you understand how the events are related to each other

zavuch27 [327]3 years ago
7 0

Answer:

a) 0.2

b) 0.2

c) 0.5

Step-by-step explanation:

Let S be the event "the car stops at the signal.

In the attached figure you can see a tree describing all possible scenarios.

For the first question the red path describes stopping at the first light but not stopping at the second. We can determine the probability of this path happening by multiplying the probabilities on the branches of the tree, thus

P(a)=0.4\times0.5=0.2

For the second one the blue path describes the situation

P(b)=0.4\times 0.5=0.2

For the las situation the sum of the two green path will give us the answer

P(c)=0.6\times 0.5 + 0.4\times 0.5=0.3+0.2=0.5

You might be interested in
The given line passes through the points (0, −3) and (2, 3).
Fed [463]
If the 2 lines are parallel, their slopes are the same.

The slope of both is  
          3+3
m = ---------- = 3
          2 - 0

If the new line <span>passes through the point (−1, −1), then the equation in point slope form is:

y+1 = 3(x+1).</span>
4 0
3 years ago
Help! This is due today and I'm stuck on this problem.
Varvara68 [4.7K]

Answer:

280.6 m^2

Step-by-step explanation:

<u>find the length of each side:</u>

you're only given h = 9 m

the formula for h is  h=\frac{\sqrt{3} }{2} *a, where a is a side length of the hexagon

plug h in:

9=\frac{\sqrt{3}}{2}*a\\\\a=9*\frac{2}{\sqrt{3}}\\\\

a ≈ 10.392 m

<u>now find the area of a triangle:</u>

1/2 (10.392)(9) = 46.764 m^2

multiply that by 6 and you get 280.584 ≈ 280.6 m^2

you can also use the regular hexagon area formula instead of finding the individual area and multiplying by 6: \frac{3\sqrt{3} }{2} *a^2

7 0
2 years ago
Read 2 more answers
7x² + 6x - 1<br> Algebra 3|factoring
GaryK [48]

Answer:

(7 x - 1) (x + 1)

Step-by-step explanation:

Factor the following:

7 x^2 + 6 x - 1

Factor the quadratic 7 x^2 + 6 x - 1. The coefficient of x^2 is 7 and the constant term is -1. The product of 7 and -1 is -7. The factors of -7 which sum to 6 are -1 and 7. So 7 x^2 + 6 x - 1 = 7 x^2 + 7 x - x - 1 = (7 x - 1) + x (7 x - 1):

(7 x - 1) + x (7 x - 1)

Factor 7 x - 1 from (7 x - 1) + x (7 x - 1):

Answer: (7 x - 1) (x + 1)

5 0
3 years ago
There are 8 pints in a gallon. How would you convert 13 pints into gallons?
Alex

Answer:

1.625 gal

Step-by-step explanation:

One pint equals 0.125 gal.

5 0
3 years ago
Ronald is calculating the time required to fill the swimming pool at school. He found that it takes 15 minutes to fill the swimm
Alik [6]

Answer:

C. 9 gallons per minute

Step-by-step explanation:

Divide 135 by 15 to see how many gallons he can fill in one minute.

135 ÷ 15 = 9

Hope this helps!

6 0
2 years ago
Other questions:
  • LITTLE HELP PLEASE!!
    14·2 answers
  • What is the percent when the balance goes from $300 to $60?
    12·2 answers
  • A soft drink costs $1.65 and each refill for the drink costs $0.95. If you have $4.50, how many refills can you purchase?
    15·2 answers
  • The<br> 10. A jet flies at an altitude of 52,800 feet.<br> What is the height of the jet in miles?
    5·2 answers
  • Flogx=219.27 , G.M = 67.19 Find f
    14·1 answer
  • Given the figures are similar, calculate the length of US
    11·1 answer
  • I need to know the answer for 15, if you can please show your work
    10·1 answer
  • How would I solve this?
    5·1 answer
  • Solve the equation. -2x + 7x + 34 = -2 ( 1 - 7 \x )
    7·1 answer
  • Round off 0.02435 to three significant and add to 0.00732​
    10·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!