Question

In a group of seven Olympic track stars, six are hurdlers. If three track stars are selected at random without replacement, find the probability that they are all hurdlers. Express your answer as a decimal rounded to four places if necessary.

P(all three hurdlers) =

Answer 1

The probability of selecting three hurdlers out of a group of seven Olympic track stars at random without replacement is calculated by multiplying the individual probabilities of selecting a hurdler each time, resulting in a probability of 0.5714.

Step-by-step explanation:

When calculating the probability of selecting three hurdlers from a group of seven Olympic track stars wherein six are hurdlers, we're dealing with a scenario of drawing without replacement. To find this probability, we need to multiply the probability of choosing a hurdler each time we select a track star.

For the first track star selected, the probability that the person is a hurdler is 6/7. Since one hurdler is chosen and not replaced, there are now five hurdlers out of six total track stars remaining. Thus, the probability of selecting another hurdler is now 5/6. If a second hurdler is selected again without replacement, there are four hurdlers left out of five. Hence, the probability of picking a hurdler again is 4/5.

To find the overall probability of picking three hurdlers in succession without replacement, we calculate the product of the individual probabilities:

P(all three hurdlers) = (6/7) × (5/6) × (4/5) = 20/35 = 0.5714

So, the probability that all three track stars selected are hurdlers is 0.5714, rounded to four decimal places.