Question

It is presentation day in class and your instructor is drawing names from a hat to determine the order of the presentations. If there are 18 studentsin the class, what is the probability that the first 2 presentations will be by Kelly and Harmony, in that order? Express your answer as a fraction inlowest terms or a decimal rounded to the nearest millionth.

Answer 1

`(1)/(306)`

Step-by-step explanation

Two events are dependent when the outcome of the first event influences the outcome of the second event. The probability of two dependent events is the product of the probability of X and the probability of Y AFTER X occurs

`P(A\text{ and B\rparen=P\lparen A\rparen *P\lparen B\rparen}`

now, the probability of an event is t is the number of favorable outcomes divided by the total number of outcomes possible.

`P(A)=\frac{favorable\text{ outcomes}}{total\text{ outcomes}}`

Step 1

find the probabily of each event

A)event: first presentation kelly

let

`\begin{gathered} favorable\text{ outcomes = 1}(\text{ kelly\rparen} \\ total\text{ outcome= 18 \lparen}total\text{ students\rparen} \end{gathered}`

now, replace

`\begin{gathered} P(A)=\frac{favorable\text{ outcomes}}{total\text{ outcomes}} \\ P(A)=(1)/(18) \end{gathered}`

b) event b, Harmony second presentation

let

`\begin{gathered} favorable\text{ outcomes = 1}(\text{ Harmony\rparen} \\ total\text{ outcome= 17\lparen}total\text{ students- Kelly\rparen} \end{gathered}`

hence

`\begin{gathered} P(B)=\frac{favorable\text{ outcomes}}{total\text{ outcomes}} \\ P(B)=(1)/(17) \end{gathered}`

Step 2

finally, do the producto of the probabilities

`\begin{gathered} P(A\text{ and B\rparen=P\lparen A\rparen *P\lparen B\rparen} \\ P(A\text{ and B\rparen=}(1)/(18)*(1)/(17) \\ P(A\text{ and B\rparen=}(1)/(306) \end{gathered}`

therefore, the answer is

`(1)/(306)`

I hope this helps you