Question

In which example are the events independent? A) Ariel has a standard deck of 52 cards. She draws one card from the deck and then replaces it. She then draws a second card from the deck. What is the probability that both cards are clubs? B) Alisa has a bag of 10 red and 6 green marbles. She takes one marble out of the bag and does not replace it. She then takes a second marble out of the bag. What is the probability that both marbles are green? C) In a bag of apples there are 4 green apples and 2 red apples. Bethany takes a green apple out of the bag and does not replace it. She then takes another apple out of the bag. What is the probability that the second apple is red? Eliminate D) In Mrs. Brown's Geometry class there are 15 boys and 10 girls. The students are presenting projects to the class. If Mrs. Brown selects students at random for presentations, what is the probability that the first 2 students chosen are girls?

Answer 1

Example A is independent

Answer 2

Answer:

The example in which the events are independent is:

Example A)

Step-by-step explanation:

Two events are said to be independent if happening of one event do not affect the occurrence of the other event.

A)

Since in example A a card is drawn and then placed back into the bag and then a second card is drawn.

So the occurrence of the first  event do not affect the second.

Since in both the events each card has a equal probability of being drawn.

Hence,  the probability that both cards are clubs will be:

$\dfrac{13}{52}\times \dfrac{13}{52}\\\\\\=\dfrac{1}{16}$

( Since there are 13 clubs out of total 52 cards in a deck)

whereas in the other three examples the occurrence of the first event will affect the occurrence of the second event, since there is no replacement.