A card is selected at random from an ordinary deck of 52 playing cards. Let E...

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A card is selected at random from an ordinary deck of 52 playing cards. Let E...

A card is selected at random from an ordinary deck of 52 playing cards. Let E be the event that the selected card is an ace and F be the event that it is a spade. Are the two events E and F disjoint? Are they independent? Why?

math Statistics-And-Probability

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Answer 1

Answer #1

P(E) =-= 52 13 ( i.e. Number of aces are 4)

$P(F)=\frac{13}{52}=\frac{1}{4}$ ( i.e. Number of spades are 13 )

$P(E\cap F)=\frac{1}{52}$

Therefore E and F are not disjoint

$P(E)\times P(F)=\frac{1}{13}\times \frac{1}{4}=\frac{1}{52}=P(E\cap F)$

Hence E and F are independent

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Answer 2

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