Can you explain to me how to do this problem below?

Question

A group of five pianists includes 2 boys and 3 girls. An instructor randomly selects one of the pianists to play the first part of a duet and a different pianist to play the second part of a duet. Use a sample space to determine whether randomly selecting a boy first and randomly selecting a girl second are independent events.

 

P(boy first) x P(girl second) =?

P(boy first and girl second) =?

And fill in the blank

P(boy first) x P(girl second)__(=,≠)___P(boy first and girl second), so the events are_________ .(independent or not independent)

Answer 1

P(boy first) x P(girl second) =?

 

The probability of a boy first is 2/5, the probability of a girl second is 3/5, multiplying gives 6/25

P(boy first and girl second) =?

Probability of boy first and girl second gives 2/5*3/4=6/20

you subtract a person from the denominator for the girl second since you already chose a guy first and you have one less person to choose from

 

If the probability was independent the two probabilities would equal. but they don't so they are dependent on each other.