I have a problem with defining the events in probaility like for this example.
In a 52-card deck, 3 cards are drawn. Calculate the probability of obtaining at least 1 ace.
I dont understand How to seperate the events
As for this example I multiplied the choice of an ace card among the four ace type cards I multiplied it by all the combinations of choosing 2 remaining cards among 51 cards and then I divided the whole by the choice of 3 cards among 52.
I would like to understand my mistake I know the solution is to use 1-p(a)
Best Answer
$P(at\ least\ one\ ace)=1-P(no\ ace)=1-\dfrac{^{48}C_3}{^{52}C_3}$
In your attempt, you found out $P(exactly\ one\ ace)$. You also need to consider 2 aces, 1 other card and 3 aces.
In total you get $={^4C_1}*{^{48}C_2}+{^4C_2}*{^{48}C_1}+{^4C_3}$
Divide this by $^{52}C_3$ to get the desired probability. Actually, the compliment method is simpler.