In a standard deck of 52 playing cards there are 13 hearts. If 3 cards are drawn from the deck ( WITHOUT REPLACEMENT, what is the probab. that all 3 cards will be hearts? which below and why?
A (13/52)cubed
B (13/52)(12/51)(11/50)
C (13/52)(13/51)(13/50)
D (13/52)(12/52)(11/52)
We all know that before we draw the first heart, there are 13 hearts out of 52 cards.
Think of how many hearts are left after the first (successful) draw, and how many cards are left in the deck for the second draw.
If you're not sure, post your answer for a check.
The correct answer is B. (13/52)(12/51)(11/50).
This is because when drawing without replacement, the probability of selecting the first heart is 13/52 (since there are 13 hearts out of 52 cards in total).
After selecting the first heart, there are now 51 cards left in the deck, with 12 hearts remaining. The probability of selecting the second heart is therefore 12/51.
After selecting the second heart, there are now 50 cards left in the deck, with 11 hearts remaining. The probability of selecting the third heart is therefore 11/50.
To find the probability of all three events happening, we multiply the individual probabilities together. Hence, the answer is (13/52)(12/51)(11/50).
To calculate the probability of drawing 3 hearts from a standard deck of 52 playing cards without replacement, you need to consider the number of favorable outcomes (drawing 3 hearts) divided by the number of possible outcomes (drawing any 3 cards).
The correct option is B: (13/52)(12/51)(11/50).
Here's why:
The first card can be any of the 13 hearts out of the 52 total cards in the deck. So, the probability of drawing a heart on the first draw is 13/52.
After the first card is drawn, there are now 51 cards remaining, of which 12 are hearts (as one heart has already been drawn). Therefore, the probability of drawing a heart on the second draw is 12/51.
Now, after two hearts have been drawn, there are 50 cards left in the deck, and 11 of them are hearts. Therefore, the probability of drawing a heart on the third draw is 11/50.
To find the probability of drawing 3 hearts together, you multiply the probabilities of each individual draw. So, the probability of drawing 3 hearts without replacement will be (13/52)(12/51)(11/50), which is option B.