Question

hello, I'm having trouble understanding how to do these two problems could you show me a step by step.

1)Eight sprinters have made it to the Olympic finals in the 100-meter race. In how many different ways can the gold, silver, and bronze medals be awarded?

2)Suppose that 34% of people own dogs. If you pick two people at random, what is the probability that they both own a dog?
Give your answer as a decimal (to at least 3 places) or fraction

   

Answer 1

Question (1)

There are 8 sprinters. There are 3 medals - Gold, Silver and Bronze

Gold Medal can be awarded to any of the 8 sprinters

Silver Medal can be awarded to any of the remaining 7 sprinters (since one of the sprinter is already awarded the gold medal)

Bronze Medal can be awarded to any of the remaining 6 sprinters (since one sprinter is already awarded gold medal and the othr is awarded silver medal)

So the total number of ways in which the Gold, Silver and Bronze medals can be awarded to 8 sprinters

= 8 * 7 * 6 = 336

Question (2)

Suppose that 34% of people own dogs.

P (Both the people owning the dogs) = P (1st person owns a dog) * P(2nd person owns a dog)

Since both the events are independent here, P(First event second event) = P(first event) * P(second event)

Probability that 1st person own a dog = 34/100 = 0.34

Probability that 2nd person own a dog = 0.34

Probability that both persons own a dog = 0.34 * 0.34 = 0.1156

= 0.116 rounded to 3 decimals