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The answer would depend on the Demographics of the population: a probability of 0.2 it too high unless the population is from a retirement area.

Q: What is the probability that in a randomly selected sample of 6 people exactly 4 of them are 65 approximately 0.2?

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The probability that exactly 4 out of 6 randomly selected vehicles will pass the test when the pass rate is 80% is approx 0.2458 (or nearly a quarter).

It is 0.0033

1 out of 3600

The probability of obtaining exactly two heads in three flips of a coin is 0.5x0.5x0.5 (for the probabilities) x3 (for the number of ways it could happen). This is 0.375. However, we are told that at least one is a head, so the probability that we got 3 tails was impossible. This probability is 0.53 or 0.125. To deduct this we need to divide the probability we have by 1-0.125 0.375/(1-0.125) = approximately 0.4286

The probability is 2 - 6

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The probability that exactly 4 out of 6 randomly selected vehicles will pass the test when the pass rate is 80% is approx 0.2458 (or nearly a quarter).

It is 3/8.

2/4

Let us assume that there are exactly 365 days in a year and that birthdays are uniformly randomly distributed across those days. First, what is the probability that 2 randomly selected people have different birthdays? The second person's birthday can be any day except the first person's, so the probability is 364/365. What is the probability that 3 people will all have different birthdays? We already know that there is a 364/365 chance that the first two will have different birthdays. The third person must have a birthday that is different from the first two: the probability of this happening is 363/365. We need to multiply the probabilities since the events are independent; the answer for 3 people is thus 364/365 × 363/365. You should now be able to solve it for 4 people.

The probability is 7:12... There are five months with less than 31 days, so the probability of selecting a month with exactly 31 days is 7 out of 12.

It is 0.0033

False. It is approximately 1. Theoretically, it is not 1. I used excel, and I know the probability is between 0.999999 and 1. as the probability of Z<6 is 0.999999. I can't calculate the probability exactly because excel only goes to 7 place accuracy.

1 out of 3600

The probability is close to 0. You would need to know details of all the companies in the world that filed reports. Chances of finding one whose profits were exactly 63% are pretty slim!

The probability of obtaining exactly two heads in three flips of a coin is 0.5x0.5x0.5 (for the probabilities) x3 (for the number of ways it could happen). This is 0.375. However, we are told that at least one is a head, so the probability that we got 3 tails was impossible. This probability is 0.53 or 0.125. To deduct this we need to divide the probability we have by 1-0.125 0.375/(1-0.125) = approximately 0.4286

The probability is 2 - 6

The probability is 0.375