Question

At the State High School Track and Field Championships, Joaquin is one of seven students to qualify for the finals of the 100 Meters race. Gold, silver and bronze medals will be awarded to the first, second, and third place finishers. Considering that there can be no ties and assuming that all runners have an equal chance of success, what is the probability that Joaquin will bring home some kind of medal in this event? (HINT: How many ways could Joaquin win a medal and how many ways can the medals be awarded?)

Answer 1

1.)

Number of players = 7

Number of medals = 3

No Player can receive more than one medal and each have equal chance of success.

So, Number of ways to distribute 3 medals to 7 people = ⁷P₃ = 7*6*5 = 210

Number of ways in which Joaquin can win any medal = 3 * ⁶P₂ = 90

So, Required Probability = 90/210 = 3/7 = 0.427

2.)

sample size , n = 50

Population Proportion, p = 39.4% = 0.394

a.) Expected value of sample = p = 0.394

b.) variance = = (0.394 * 0.606) / 50

Р(1 — р) п

variance = 0.0047752

Standard deviation = $\sqrt{variance}$ = 0.0691