Question

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?

Answer 1

Yes, it is correct....

Answer 2

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

`P(A)=(1)/(4),`

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

`P(B)=(3)/(13).`

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

`P(A\cap B).`

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

Therefore, we have

`P(A\cap B)=P(A)P(B)=(1)/(4)* (3)/(13)=(3)/(52).`

Thus, Drew is absolutely CORRECT.