Question

Of 80 people attending a dance 28 dance with their hands touching the floor. If four people at the dance are selected at random, determine the probability that each of the 4 dance with their hands touching the floor.

`PLEASE HURRY ITS A QUIZ

Answer 1

The probability that each of the 4 dance with their hands touching the floor is 0.0129.

Explanation:

There are a total of 80 people and out of them, 28 dance with their hands touching the floor. The probability of selecting a person who has their hands touching the floor while dancing can be computed as 28/80.

We are asked to computed the probability that four people are selected at random and all four of them dance with their hands touching the floor. The probability for selecting the first person is 28/80. For the second person, the total no. of people are now 79 and the people who can dance with their hands touching the floor are 27. So, the probability is 27/79. Similarly, for the third person, the probability is 26/78 and for the fourth person, the probability is 25/77.

So, the probability that all four people selected dance with their hands touching the floor is:

28/80 * 27/79 * 26/78 * 25/77 = 0.0129

Answer 2

Answer: The probability is 0.013

Explanation:

Out of 80 people, 28 of them dance with the hands touching the ground.

Then, the probability of selecting at random someone that dances with the hands touching the floor is equal to the number of persons that dance in that way, divided by the total number of persons.

For the first selection, this is p1 = 28/80

now, the probability in the second selection will be 27/79, because we have selected 1 out of the 28 (and also 1 out of the 80)

for the third and the fourth we have:

p3 = 26/78

p4 = 25/77

Then the probability of the fourth events is equal to the product of the four probabilities:

P = (28/80)*(27/79)/(26/78)/(25/77) = 0.013