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One card is drawn at random from a well shuffled deck of 52 cards. Is following cases are the events E and F independent?
 E: ‘the card drawn is a king or queen’
 F: ‘the card drawn is a queen or jack’

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Event E :  Card drawn is king or queen

Event F :  Card drawn is queen or jack

Independent event : We say two events are independent if happening of one , doesn't effect the chances of happening of other. Like if India's capital is  place X , you will drink milk :) funny :) they are independent i suppose.

another example is You throw a dice , every time 6 possibilities are there and they are independent , if this time 4 came , then in next throw , any thing can come.

Now come to your question.

There if you replace the card after outcome , they are Independent 

If you don't replace , and put that card with you and choose one out of remaining cards , both event can never be independent.

In mathematical terms you say two Event E,F are independent iff P(E/F)=P(E)

which you can see P(K/Q)=8/52      P(Q/J)=8/52

BUt if you don't place outcome of event E and if outcome is K then P(Q/J)=8/51 and if outcome of event E is Queen then P(Q/J)=7/51

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  • If A and B are independent events, \(P(A\cap\;B)=P(A)\;P(B)\)

Given a deck of 52 cards, there are 4 kings, 4 queens and 4 jacks, and the P(drawing a king) = P(drawing a queen) = P(drawing a jack) = 4/52=1/13 assuming replacement.

Given E: the card drawn is a king or queen, P (E) = P(king) + P(queen) = 1/13+1/13=2/13

Given F: the card drawn is a queen or a jack, P(F) = P(queen) + P(jack) = = 1/13+1/13=2/13

If A and B are independent events, \(P(A\cap\;B)=P(A)\;P(B)\)

P (E ∩F)=P(card_drawn_queen)=4/52=1/13.  ____(1)

P (E ∩ F) = P(E) × P(F) = (2/13)*(2/13)=4/169____(2)

comparing equation 1 and 2: (1/13) ≠ ((4/169)

Therefore E and F are NOT independent.

Thanks and and this is my first answer so upvote if you like.

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