Danielle may choose one of two options for the method in which she may be awarded a money prize.

option a: spin a spinner twice. the spinner is divided into four equally-sized sectors numbered 1, 4, 4, and 5. if the sum of the two spins is greater than 6, danielle is awarded $8. otherwise, shee must pay $2.

option b: flip a coin three times. if heads appears once, danielle is awarded $6. otherwise, she must pay $1.

danielle chooses the option with the greater mathematical expectation. how much more money can danielle expect to make by choosing this option over the other option?

$2

Step-by-step explanation:

I've just taken the quiz and it is $2

Option B

Step-by-step explanation:

Because if danielle chose option b she has 3 chances to get $6 she will get $18 ( -$1 per heads) so thats $15, option a has to be GREATER that 6 which is only 2 options (4+4=8, and 5+4=9) then she will get $8 (-$2 dollars for greater number than 6) which will only get her $6

a) one student is chosen from classroom a, then a student is chosen from classroom b.  

step-by-step explanation:

independent events are ones in which the probability of one event does not affect the probability of the second event.

one student is chosen from classroom a; this does not affect the chances of choosing a student from classroom b.   this makes these independent events.

when one card is chosen from a standard deck and then set aside before a second card is chosen, the probability of the second card being chosen changes.   this makes them dependent events.

when one student is chosen from classroom a and then a second student is chosen from classroom a, the probability of choosing the second student changes.   this makes them dependent events.

when a letter is chosen from the alphabet and then a second letter is chosen, the probability of choosing the second letter changes.   this makes them dependent events.

answer: a.

step-by-step explanation: the answer is a. because, you need to converge the fractions to find a solution.