Answer to Question #347001 in Statistics and Probability for Nzuzi

Question

Question 1.13 [2, 2, 3]

Due to COVID-19 there was no time to have the swimming gala at your old primary school. The

principal knows that you are currently studying statistics and he wants you to help with this

probability problem. The principal tells you that out of the 8 swimmers, 3 are from grade 4, 2 are

from grade 5 and 3 are from grade 6. Since no Gala can be held the principal selects swimmers at

random to attend the EP school Gala, the first student selected at random will be representing the

schools fastest swimmer, while the second student selected will represent the school second fastest

swimmer.

Help the principal to answer the following questions:

a) What is the probability that the two fastest swimmers are from Grade 6?

b) What is the probability that fastest swimmer is from Grade 4 and the second fastest from

Grade 6?

c) Timothy is a student in grade 5, what is the probability that he will either come first or second?

Answer 1

a)

$$P(6\&6)=\dfrac{3}{8}(\dfrac{2}{7})=\dfrac{3}{28}$$

b)

$$P(4\&6)=\dfrac{3}{8}(\dfrac{3}{7})+\dfrac{3}{8}(\dfrac{3}{7})=\dfrac{9}{28}$$

c)

$$P(Timothy)=\dfrac{\dbinom{7}{1}}{\dbinom{8}{2}}=\dfrac{1}{4}$$