A defective car has a probability of 2/3 upon turning on the ignition in each attempt....

A defective car has a probability of 2/3 upon turning on the ignition in each attempt. Assume attempts

are independent.

• (a) What is the probability that exactly 3 attempts are needed until the car starts?

• (b) What is the probability that 3 or 4 attempts are needed?

• (c) What is the probability of success in 4 or more trials?

Expert Solution

By using multiplication theorem of probability of independent event, we will solve.

Probability that car starts in 1 attempt= probability of turning on to ignition temperature=P=2/3

So, probability that car not starts in a attempt=q=(1-p)=1-2/3=1/3

a) Ans- the car starts in exactly three attempts if in the first two attempts it doesn't starts. So, by using multiplication theorem of probability of independent event.

This, probability that exactly three attempts are needed until the car starts=(1/3)*(1/3)*(2/3)=2/27

b) Ans- probability that 3 or 4 attempts needed=probability that 3 attempts needed+probability that 4 attempts needed=(1/3*1/3*2/3)+(1/3*1/3*1/3*2/3)=2/27+2/81=8/81

c) Ans-probability of success in 4 or more trials=1- probability of success in less than or equal to 3 trials=1- {p(success in 1 trial)+P(success in 2 trials)+P(probability of success in 3 trials)}=

1-{(2/3)+(1/3*2/3)+(1/3*1/3*2/3)}=1-(2/3+2/9+2/27)=1-(26/27)=1/27

milcah answered 1 year ago

A bias coin has the probability 2/3 of turning up heads. The coin is thrown 4...

A bias coin has the probability 2/3 of turning up heads. The coin is thrown 4 times. (a) What is the probability that the total number of heads shown is 3? (b) Suppose that we know that outcome of the first throw is a head. Find the probability that the total number of heads shown is 3. (c) If we know that the total number of heads shown is 3, find the probability that the outcome of the first throw...

7. A certain sports car model has a 0.07 probability of defective steering and a 0.11...

7. A certain sports car model has a 0.07 probability of defective steering and a 0.11 probability of defective brakes. Erich S -E just purchased one of the models. If the two problems are statistically independent, determine the probability a. Erich’s car has both defective steering and defective brakes. b. Erich’s car has neither defective steering nor defective brakes. c. Erich’s car has either defective steering only or defective brakes only (meaning exactly one of the two, but not both,...

3) A car turning in a circle is acceleratring in the centripetal direction, even if the...

3) A car turning in a circle is acceleratring in the centripetal direction, even if the speed is constant. This centripetal acceleration is the cause of a radially inward directed net force. On a level road this net force is the friction force acting from the road on the tires. You already looked at examples for this. On racetracks and also highway turns the reliance on friction can be reduced by "banking" the road. This also reduces the risk of...

Container 1 has 8 items, 3 of which are defective. Container 2 has 5 items, 2...

Container 1 has 8 items, 3 of which are defective. Container 2 has 5 items, 2 of which are defective. If one item is drawn from each container, what is the probability that only one of the items is defective?

A factory that puts together car parts is known to produce 3% defective cars. Following a...

A factory that puts together car parts is known to produce 3% defective cars. Following a fire outbreak at the factory, reconstruction is carried out which may result in a change in the percentage of defective cars produced. To investigate this possibility, a random sample of 200 cars is taken from the production and a count reveals 14 defective cars. What may be concluded? Run a significance test using a 0.05 α-level of significance.

A 3-person jury has 2 members each of whom have independently a probability 0.7 of making...

A 3-person jury has 2 members each of whom have independently a probability 0.7 of making a correct decision. The third juror just flips a coin for each decision. In this jury, the majority rules. A 1-person jury has a probability 0.7 of making a correct decision. What is the probability of the best jury of making a correct decision?

Assume that light bulbs bought at a supermarket have a probability 1/3 of being defective. 1）If...

Assume that light bulbs bought at a supermarket have a probability 1/3 of being defective. 1）If you buy 10 light bulbs, what is the probability that 3 are defective? 2）If you buy one light bulb per day, what is the probability that the first defective one is on day three? 3）If you buy one light bulb per day, and the one bought on day one was defective, what is the probability that the next defective one is on day 5?

1) a) A certain kind of light bulb has a 8.5 percent probability of being defective....

1) a) A certain kind of light bulb has a 8.5 percent probability of being defective. A store receives 54 light bulbs of this kind. What is the expected value (or mean value) of the number of light bulbs that are expected to be defective? b) In a certain town, 19 % of the population develop lung cancer. If 25 % of the population are smokers and 85% of those developing lung cancer are smokers, what is the probability that...

A widget produced by a particular process has probability .1 of being defective. A test can...

A widget produced by a particular process has probability .1 of being defective. A test can be performed which has 99% accuracy. That is, if a defective widget is tested, the test will identify the widget as defective 99% of the time. And if a non-defective widget is tested, there is a 99% chance that the test will indicate that the widget is not defective. One widget is selected at random and is tested. If the test says that the...

1. A factory manufactures machines. Each machine is defective with probability 1/100, independently. The machines get...

1. A factory manufactures machines. Each machine is defective with probability 1/100, independently. The machines get numbered 1, 2, . . . as they’re produced (a) Out of machines 1, . . . , 1000, what is the probability that none are defective? (b) Out of machines 1, . . . , 1000, what is the probability that two or fewer are defective? (c) Out of machines 1, . . . , 1000, what is the probability that exactly ten...

Question