Mathematics, 20.02.2020 20:53 tressasill

Seventy percent of all vehicles examined at a certain emissions inspection station pass the inspection. Assuming that successive vehicles pass or fail independently of one another, calculate the following probabilities
(a) P(all of the next three vehicles inspected pass)
(b) P(at least one of the next three inspected fails
(c) P(exactly one of the next three inspected pass)
(d) P(at most one of the next three vehicles inspected passes)
(e) Given that at least one of the next three vehicles passes inspection, what is the probability that all three pass (a conditional probability)?

Answers: 3

Show answers

Answers

Answer from: abcdefg87

a. 0.343

b. 0.657

c. 0.189

d. 0.216

e. 0.353

Step-by-step explanation:

We use the combination formula of probability distribution to solve the question.

Where P(x=r) = nCr * p^r * q^n-r

Where n = number of trials = 3 vehicles

r = desired outcome of trial which varies.

p = probability of success = 70% =0.7

q = probability of failure = 1-p = 0.3

a. Probability that all 3 vehicles passed = P(X=3)

= 3C3 * 0.7^3 * 0.3^0 = 1 * 0.343 * 1

= 0.343.

b. Probability that at least one fails = 1 - (probability that none failed)

And probability that none failed = probability that all 3 vehicles passed.

Hence Probability that at least one fails = 1 - (probability that all 3 vehicles passe)

= 1 - 0.343

= 0.657

c.) probability that exactly one pass= P(X=1)

= 3C1 * 0.7¹ * 0.3² = 3 * 0.7 * 0.09

= 0.189

d.) probability that at most One of the vehicles passed = probability that none passed + probability of one passed.

Probability that none of the vehicles passed = P(X=0)

= 3C0 * 0.7^0 * 0.3^3 = 1*1*0.027

=0.027

Probability that one passed as calculated earlier = 0.189

Hence probability that at most one vehicle passed = 0.189 + 0.027 = 0.216

e.) Probability that all three Vehicles pass given that at least one pass = (probability of all three vehicles passes) / (probability that at least one passes)

Probability that at least one pass = 1 - probability that none passed.

= 1 - 0.027

= 0.973

Hence,

Probability that all three Vehicles passed given that at least one passed = 0.343/0.973

= 0.3525 = 0.353 (3.d.p)

Answer from: Quest

first one is a: renaming a fraction. second one is c: de-c

step-by-step explanation:

my explanation is that these were the answers on edg : )

Answer from: Quest

First step is to get rid of the square root. remember that a square root is the same as raising to the (1/2) power. see below: $\sqrt{\frac{ {72x}^{16} }{ {50x}^{{{36} }}}} = \frac{ { \sqrt{72}x}^{ {16}^{ (\frac{1}{2}) } } }{ { \sqrt{50} x}^ {{36}^{ (\frac{1}{2}) } }}$ multiply exponents per exponent rules to get: $\frac{ { \sqrt{72}x}^{8} }{ { \sqrt{50}x}^{18} }$ remember you subtract exponents from the denominator and add exponents in the numerator so: $\sqrt{ \frac{72}{ 50}} \times ( {x}^{(8 - 18) } ) = \sqrt{ \frac{36}{25} } \times ( {x}^{ - 10} )$ simplify further: $\frac{6}{5} {x}^{ - 10} = \frac{6}{5 {x}^{10} }$ so a is the correct choice. if you don't understand this google exponent rules and it will you understand. look at the image results.
Plz hurrywhat is the simplified form of ? assume x ≠ 0.

Plz hurrywhat is the simplified form of  ? assume  x  ≠ 0.

Another question on Mathematics

Mathematics, 21.06.2019 18:00

Arecipe calls for 2 2/4 cups of raisins, but julie only has a 1/4 measuring cup. how many 1/4 cups is needed to measure out 2 2/4 cups of raisins?

Answers: 1

Answer

Mathematics, 21.06.2019 18:10

Josh has a rewards card for a movie theater he receives 15 points for becoming a rewards card holder he earns 3.5 points for each visit to the movie theater he needs at least 55 points to earn a free movie ticket which inequality can josh use to determine x, the minimum number of visits he needs to earn his first free movie ticket.

Answers: 1

Answer

Mathematics, 21.06.2019 19:00

What is the simplified form of (3.25x10^3)(7.8x10^6) written in scientific notation?

Answers: 1

Answer

Mathematics, 21.06.2019 21:00

Simplify -4z+2y-y+-18z a.-22z+y b.-14z+2 c.3y+22z d.y +14z

Answers: 1

Answer

You know the right answer?

Seventy percent of all vehicles examined at a certain emissions inspection station pass the inspecti...