Question

Which of the following events has an expected value that is in the sample space? A. tossing a number cube once B. flipping a coin C. randomly picking a number between one and nine, inclusive D. randomly picking a number between one and ten, inclusive

Answer 1

the answer is D because i used common sense i guess

Answer 2

A) The event is "tossing a number cube once"

The sample space of this event is {1,2,3,4,5,6}.

The expected value of this event is

`1* (1)/(6)+2* (1)/(6)+3* (1)/(6)+4* (1)/(6)+5* (1)/(6)+6* (1)/(6)\\ \\ =(1)/(6)+(1)/(3)+(1)/(2)+(2)/(3)+(5)/(6)+1\\ \\ =(7)/(2) = 3.5`

Since 3.5 is not in the sample space of the event. Therefore, option (A) is not correct.

(B) The event is "Flipping a coin"

Sample space of this event is {HH,TT,HT,TH}

Since sample space of this event is not numbers, therefore, this cannot be the correct option either.

(C) The event is, "Randomly picking a number between 1 and 9, inclusive."

The sample space of this event is {1,2,3,4,5,6,7,8,9}.

Expected value of this event is
`(1)/(9)(1+2+3+4+5+6+7+8+9) = (1)/(9)(45) = 5`

Since 5 is the expected value and it is present in the sample space for this event. Therefore, option (C) is a correct choice.

(D) The sample is "Randomly picking a number between one and ten, inclusive".

The sample space of this event is {1,2,3,4,5,6,7,8,9,10}.

Therefore, expected value of the event is
`(1)/(10)(1+2+3+4+5+6+7+8+9+10) = (1)/(10)(55)=5.5`

Since 5.5 is not present in the sample space of this event. Therefore, option (D) is not correct either.

Hence, the correct choice is option (C).