Mathematics, 26.12.2019 19:31 reinasuarez964

There are two traffic lights on the route used by a certain individual to go from home to work. let e denote the event that the individual must stop at the first light, and define the event f in a similar manner for the second light. suppose that p(e) = .4, p(f) = .2 and p(e intersect f) = .15.
(a) what is the probability that the individual must stop at at least one light; that is, what is the probability of the event p(e union f)?

(b) what is the probability that the individual needn't stop at either light?

(c) what is the probability that the individual must stop at exactly one of the two lights?
3

(d) what is the probability that the individual must stop just at the first light? (hint: how is the probability of this event related to p(e) and p(e intersect f)? a venn diagram might .)
4

Answers: 1

Show answers

Answers

Answer from: hellicuh

a) There is a 45% probability that the individual must stop at at least one light.

b) 55% probability that the individual needn't stop at either light.

c) 30% probability that the individual must stop at exactly one of the two lights.

d) 25% probability that the individual must stop just at the first light.

Step-by-step explanation:

The problem says that:

P(E) is the probability that a person has to stop at the first light.

P(F) is the probability that a person has to stop at the second light.

We have that:

$P(E) = P(e) + P(E \cap F)$

In which P(e) is the probability that a person has to stop at the first light but not the second and $P(E \cap F)$ is the probability that a person has to stop at both these lights

By the same logic, we have that:

$P(F) = P(f) + P(E \cap F)$

Lets find each value:

$P(E \cap F) = 0.15, P(F) = 0.2, P(E) = 0.4$

$P(F) = P(f) + P(E \cap F)$

0.2 = P(f) + 0.15

P(f) = 0.05

---------

$P(E) = P(e) + P(E \cap F)$

0.4 = P(e) + 0.15

P(e) = 0.25

(a) What is the probability that the individual must stop at at least one light; that is, what is the probability of the event P(E union F)?

This is

$P = P(e) + P(f) + P(E \cap F) = 0.05 + 0.25 + 0.15 = 0.45$

There is a 45% probability that the individual must stop at at least one light.

(b) What is the probability that the individual needn't stop at either light?

Either a person has to stop in at least one light, or the person does not have to stop at any.

The sum of these probabilities is decimal 1. So this probability is 1 subtracted by the probability found in a).

So 1-0.45 = 0.55 = 55% probability that the individual needn't stop at either light.

This is P(e) + P(f) = 0.25 + 0.05 = 0.30 = 30% probability that the individual must stop at exactly one of the two lights.

(d) What is the probability that the individual must stop just at the first light?

This is P(e) = 0.25.

So there is a 25% probability that the individual must stop just at the first light.

Answer from: Quest

Where the white dots are is where your points should be plotted.a translation is simply just moving something from one place to another. in this case, you would move each plot point of the original shape 2 units up, and 5 units to the left.

Answer from: Quest

X= 2 he can buy 2 packs of cards for $12 and an action figure for $3 so he would spend $15 in total plus the free poster

Another question on Mathematics

Mathematics, 21.06.2019 15:50

Assemble the proof by dragging tiles to the statements and reasons column

Answers: 2

Answer

Mathematics, 21.06.2019 16:30

Hillel is juggling flaming torches to raise money for charity. his initial appearance raises $500\$500 $500 , and he raises $15\$15 $15 for each minute of juggling performance. the amount rr r of money hillel raises is a function of tt t , the length of his performance in minutes. write the function's formula.

Answers: 1

Answer

Mathematics, 22.06.2019 00:20

Which shows how to solve the equation 3/4x=6 for x in one step?

Answers: 2

Answer

Mathematics, 22.06.2019 01:00

Ataxi company charges $3 for pick-up plus $0.65 for each mile. select the expressions that represent the cost in dollars for a taxi pick-up and m miles. mark all that apply.

Answers: 1

Answer

You know the right answer?

There are two traffic lights on the route used by a certain individual to go from home to work. let...

Questions