Mathematics, 31.03.2020 02:28 cvvalle15

The probability that a certain make of car will need repairs in the first six months is 0.4. A dealer sells seven such cars. What is the probability that at least one of them will require repairs in the first six months?

Answers: 1

Show answers

Answers

Answer from: supercutedonuf3753

0.972

Step-by-step explanation:

This problem can be solved binomialy with n = 7

The probability that the car will need repair ; p(need repair) = 0.4

The probability that the car will not need repair ; p(no repair) = 1 - 0.4 = 0.6

Probability at least 1 will need repair = 1 - Probability none will need repair

Probability at least 1 will need repair = 1 - p(no repair)

= $1-(0.6)^{7} = 0.972$

$\therefore$ The probability that at least one of them will require repairs in the first six months is 0.972

Answer from: trippie4life

Probability that at least one of them will require repairs in the first six months is 0.972.

Step-by-step explanation:

We are given that the probability that a certain make of car will need repairs in the first six months is 0.4. A dealer sells seven such cars.

The above situation can be represented through Binomial distribution;

$P(X=r) = \binom{n}{r}p^{r} (1-p)^{n-r} ; x = 0,1,2,3,.....$

where, n = number of trials (samples) taken = 7 cars

r = number of success = at least one

p = probability of success which in our question is probability that a

make of car will need repairs in the first six months, i.e; 0.40

LET X = Number of cars that require repairs in the first six months

So, it means X ~ Binom(n=7, p=0.40)

Now, Probability that at least one of them will require repairs in the first six months is given by = P(X $\geq$ 1)

P(X $\geq$ 1) = 1 - P(X = 0)

= $1- \binom{7}{0}\times 0.40^{0} \times (1-0.40)^{7-0}$

= $1-( 1 \times 1 \times 0.60^{7})$

= $1-0.60^{7}$ = 0.972

Therefore, Probability that at least one of them will require repairs in the first six months is 0.972.

Answer from: Quest

For the first question the answer is a, for the second c, for the third d, for the 4th b, for the 5th a

Answer from: Quest

step-by-step explanation:

Another question on Mathematics

Mathematics, 21.06.2019 18:30

Which of the statements about the graph of the function y = 2x are true? check all of the boxes that apply. the domain is all real numbers x because the exponent of 2 can be any real number when the x-values increases by 1 unit, the y-value multiplies by 2. the y-intercept is (0, 1). the graph never goes below the x-axis because powers of 2 are never negative. the range is all real numbers.

Answers: 1

Answer

Mathematics, 21.06.2019 20:10

The population of a small rural town in the year 2006 was 2,459. the population can be modeled by the function below, where f(x residents and t is the number of years elapsed since 2006. f(t) = 2,459(0.92)

Answers: 1

Answer

Mathematics, 21.06.2019 22:00

James is playing his favorite game at the arcade. after playing the game 33 times, he has 88 tokens remaining. he initially had 2020 tokens, and the game costs the same number of tokens each time. the number tt of tokens james has is a function of gg, the number of games he plays

Answers: 1

Answer

Mathematics, 21.06.2019 22:30

How can constraints be used to model a real-world situation?

Answers: 1

Answer

You know the right answer?

The probability that a certain make of car will need repairs in the first six months is 0.4. A deale...

Questions

Mathematics, 04.01.2020 02:31

The air in a small room 12ft by 8ft by 8ft is 3% carbon monoxide. starting at t=0, fresh air containing no carbon monoxide is blown into the room at a...