Two cards are chosen at random from a standard deck of cards with replacement. What is the probability of getting 2 aces?
Is is an independent events? If it is then would it be 2/52(chances of an ace) x 2/52?
since you are replacing it, the second event is not affected by the result of the first event, so the events are independent.
Prob = 4/52 x 4/52
= 16/2704
= 1/169
(why do you have 2/52 ? Aren't there 4 aces?)
I confused the PROBABILITY OF GETTING 2 ACES. Thank you very much.
Could you review this one too please.
A jar hold 15 red pencils and 10 blues pencils. What is the probability of drawing two red pencil form the jar?
This would be an dependent and it would be 15/25( first time) x 14/24(second time)?
correct! reduce it to 7/20
Thanks for the help, Reiny.
That is very correct 7/20 I've been a math teacher for over 30 years. And I had my students do 9-7 Independent And Dependent Events And we did 1-9 togather. So then I said 10 is a hard one i'm gone let them sweat. I know why you get 15/25 because 15 red pencils and add 15+10=25 so then that's 15/25 * 14/24 = 7/20 . Have a nice day. But it's not cool to get answers off the internet your math teacher will think you really really tried. But okay.
To calculate the probability of getting 2 aces when choosing 2 cards from a standard deck of cards with replacement, you can use the following steps:
Step 1: Determine the probability of getting an ace on the first draw.
In a standard deck of 52 cards, there are 4 aces. Therefore, the probability of getting an ace on the first draw is 4/52.
Step 2: Since we are replacing the cards after each draw, the deck remains the same for the second draw. So, the probability of getting an ace on the second draw is also 4/52.
Step 3: To find the probability of both events occurring, multiply the probabilities of each event together.
The probability of getting 2 aces is (4/52) * (4/52) = 16/2704, which simplifies to 1/169.
Now, regarding the question of whether the two events (drawing the first ace and drawing the second ace) are independent, the answer is yes. Here's why:
Two events are considered independent if the outcome of one event does not affect the outcome of the other event. In this case, the probability of drawing an ace on the second draw does not depend on whether an ace was drawn on the first draw because the deck is placed back together and remains the same.
Therefore, you can indeed calculate the probability of getting 2 aces by multiplying the probabilities of each event together: (2/52) * (2/52) = 1/169.