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mathmath333 one year ago Probablity question

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1. mathmath333

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

2. anonymous
3. triciaal

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4. mathmath333

how do i calculate $$P(K\cap Q)$$

5. mathmath333

P(K$$\cup$$Q)=P(K)+P(Q)-P(K$$\cap$$Q)

6. triciaal

first let me remind you I am not the best stats person

7. triciaal

|dw:1439917813910:dw|

8. anonymous

Events are independent if one does not affect the other.

9. freckles

$(\text{Q} \text{ or } \text{K}) \text{ and } (\text{Q} \text{ or } \text{J}) \\ =Q \text{ or } (K \text{ and } J) \text{ by distributive law }\\ =Q \text{ or } \emptyset \text{ since a card cannot be both a king and a jack} \\ = Q$ to check this one to see if it is independent you can see if the following equality holds: $P((\text{Q} \text{ or } K) \text{ and } (\text{Q} \text{ or } \text{J}))=P(\text{Q} \text{ or } \text{K}) \cdot P(\text{Q} \text{ or } \text{J}) \\ \\ \text{ we know the left hand side just equals } P(\text{Q}) \\ \\ \text{ and we know } P(\text{Q})=\frac{4}{52}=\frac{1}{13} \\ \text{ so check to see if the right hand side is also } \frac{1}{13}$

10. freckles

you should see it is not by what was worked out above

11. freckles

if the equality holds then E and F are independent if the equality fails then E and F aren't independent

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