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the probability of drawing a heart from a standard deck of 52 playing cards is 1/4. The probability of drawing a face card from a standard deck of 52 playing cards is 3/13. Based on this, Drew determines that the probability of drawing a heart face card is 3/52. Is this correct?

Respuesta :

Yes, it is correct....

Answer:  The answer is YES.

Step-by-step explanation:  Let 'A' and 'B' represents the events of drawing a heart and a face card respectively from a standard deck of 52 playing cards.

Then, the probability of drawing a heart from a standard deck of 52 playing cards is

[tex]P(A)=\dfrac{1}{4},[/tex]

and the probability of drawing a face card from a standard deck of 52 playing cards is

[tex]P(B)=\dfrac{3}{13}.[/tex]

So, the probability drawing a heart face card will be given by

[tex]P(A\cap B).[/tex]

Since we cannot draw a card that is both heart and face card, so the events 'A' and 'B' are independent.

Therefore, we have

[tex]P(A\cap B)=P(A)P(B)=\dfrac{1}{4}\times \dfrac{3}{13}=\dfrac{3}{52}.[/tex]

Thus, Drew is absolutely CORRECT.

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