Question

Two cards are drawn without replacement from a well-shuffled deck of 52 playing cards. What is the probability that the first card drawn is a Heart and the second card drawn is not a Heart?a) 0.1875b) 0.0577c) 0.1912d) 0.7500e) 0.0588

Answer 1

Answer:

$P(Heart)*P(No Heart) = \frac{1}{4} \frac{39}{51}=\frac{13}{68}=0.1912$

So the best option is c) 0.1912

Step-by-step explanation:

For this case we have a standard deck of 52 cards and we consider the experiment without replacement.

So then we have 13 heart cards and 52-13 = 39 NOT heart cards

In order to find the probability that we select a heart card in the first extraction we have this:

$P(Heart) =\frac{13}{52}=\frac{1}{4}$

Now for the second extraction we have a total of 51 cards since we select one at the first extraction and we can find the probability of not heart like this:

$P(No heart)= \frac{39}{51}$

And for this case we can assume that we have independent events since the extraction of the first and second card are not related events and assuming this we have this probability:

$P(Heart)*P(No Heart) = \frac{1}{4} \frac{39}{51}=\frac{13}{68}=0.1912$

So the best option is c) 0.1912