Tuck is doing a magic trick with cards. He uses a standard deck of 52 cards. He asks Ryan to select two cards without replacing them. What is the probability of Ryan selecting a heart, and then selecting a club? (Hint: there are 13 clubs, 13 diamonds, 13 hearts, 13 spades in a deck of cards)
Do you have answer choices?
I'd think it would have something to do with some kind of ratio or fraction maybe but I'm not sure without the answer choices.
A. 13/52 * 13/52
B. 13/52 + 13/52
C. 13/52 * 13/51
D. 13/51 + 13/51
the first one is 13 hearts / 52 total
now you have 13 clubs / 51 total
so
13/52 * 13/51
C
To find the probability of Ryan selecting a heart and then selecting a club without replacement, we need to calculate the probability of each event separately and then multiply them together.
First, let's find the probability of Ryan selecting a heart on the first draw. There are 13 hearts in a standard deck of 52 cards, so the probability of Ryan selecting a heart as his first card is 13/52.
After Ryan has selected a card, there are now 51 cards left in the deck, of which 13 are clubs. So the probability of Ryan selecting a club on his second draw is 13/51.
To find the probability of both events happening, we multiply the individual probabilities:
Probability = (13/52) * (13/51)
Now if we simplify this expression, the probability of Ryan selecting a heart and then a club without replacement is:
Probability = (13 * 13) / (52 * 51)
Probability = 169 / 2652
Probability ≈ 0.0637
Therefore, the probability of Ryan selecting a heart and then selecting a club without replacement is approximately 0.0637, or about 6.37%.