Question

a) Peter is involved in a swimming competition. There are 8 boys swimming in the first race. He has to be able to get a first or second in the first race to be able to go to the next level of the competition. Assuming there are no equal places, what is the probability that Peter will get first or second place?

b) Peter’s team came first out of all the teams at the swimming competition. To celebrate the team goes out for pizza and ice cream afterwards. Peter’s team has 20 people: 8 people order pizza and 12 people order ice cream. 5 people on the team also ended up ordering both pizza and ice cream. What is the probability of a person on the team ordering pizza or ice cream, but not both?

Answer 1

(a) Probability of peter getting any position is equally likely since there is no biasness.

Total no. of Possible positions = 8 also equal to total no . of outcomes

Positions that Peter is supposed to come = first and second

NO .of Possible Positions Peter is supposed to come = 2

(b) Total no. of People = 20

   NO. of people who had Pizza = 8

No. of People who had icecream = 20

Let Event A be that a person ordered Pizza

Event B be that a Person ordered Icecream

   So Probability of Event A occuring = P(A) =

   Probability of Event B occuring = P(B) =

  

Probability of People ordering both Pizza and Icecream =

  

Showing it using Venn diagram

   means A and B both , represented by white portion between both sets

Now we need the orange shaded part that represents only A and only B

   P(only A ) = P(A) - P() =

P (only B ) = P(B) - P() =

   P(only A or only B ) = P(only A U only N) = P(only A ) +P(only B) - P(only A only B)

( U symbol is union which means or in statistics )

   since there is nothing in commong between only A and only B so P(only A only B) = 0

   P( only a or only B ) =