Determine whether the events are independent.
-When a coin is tossed three times, eight equally likely outcomes are possible.
HHH HHT HTH HTT
THH THT TTH TTT
Let
$A =$ event the first two tosses are the same
$B =$ event the total number of heads is one.
Are $A$ and $B$ independent events?

Question

Determine whether the events are independent.
-When a coin is tossed three times, eight equally likely outcomes are possible. 
HHH HHT HTH HTT
THH THT TTH TTT
Let
$A =$ event the first two tosses are the same
$B =$ event the total number of heads is one.
Are $A$ and $B$ independent events?

Quizplus · Accepted Answer

Events $A$ and $B$ are not independent because the occurrence of event $A$ affects the probability of event $B$ occurring. If the first two tosses are the same (event $A$), it's impossible to have exactly one head in total (event $B$), since you already have either two heads or two tails from the first two tosses.

Determine Whether the Events Are Independent A=A =A= Event the First Two Tosses Are the Same

Determine Whether the Events Are Independent $A =$ Event the First Two Tosses Are the Same