Which describes independent events?
a. you grab two jelly beans from a jar at the same time
b. you draw a card from a deck, replace it, and draw a second
c. you draw a card and do not replace it. Then yo draw another
d. you study english every night and then you get an A on the next test
i think it is C.
Answer
B - By returning the card you have an equal change of drawing the cards as you did when your started. Making the two events independent
Explanation
For C - the card you took out changes the next draw, you are now not able to draw that card on the second turn, thus making the second draw dependent on what card was pulled out on the first draw
For D - it implies that it is dependent, it implies that your studying gave a result to your test
For A - It is a little more complicated, but what you draw is dependent on the fact that you are drawing two at once. "let me explain" - Say you have a Red, Green, and a Blue jellybean. By drawing two at once, it prevents you from drawing two of the same color, thus removing an option ( drawing a RR, GG, or BB). You can not draw two RED jelly beans, nor two any of the same color, because you are taking 2 at once. This is true for any number, and color of jellybeans. (though you now can draw 2 of the same color, the fact that your drawing 2 effect probability of what your are drawing)
B. Not replacing the card changes the probability of drawing a second.
It is not C.It is B you draw a card from a deck, replace it, and draw a second.
It is C. The card is removed, but it is replaced, leaving the chances of drawing any card the same, as it is random
To determine which scenario describes independent events, we need to understand what "independent events" means. Independent events are events where the outcome of one event does not affect the probability of the other event.
a. In scenario a, you grab two jelly beans from a jar at the same time. Since you are grabbing both jelly beans simultaneously, the outcome of grabbing one jelly bean does not affect the probability of grabbing the other jelly bean. This is an example of independent events.
b. In scenario b, you draw a card from a deck, replace it, and draw a second card. By replacing the card back into the deck before drawing the second card, the outcome of the first draw does not affect the probability of the second draw. This is also an example of independent events.
c. In scenario c, you draw a card from a deck and do not replace it, then draw another card. Since the first card is not replaced before drawing the second card, the probability of drawing the second card is affected by what was drawn in the first draw. This is an example of dependent events.
d. In scenario d, you study English every night and then get an A on the next test. This is not an example of independent events since your studying could have influenced the outcome of your test grade.
So, the correct answer is either a or b, as both scenarios describe independent events.