mathmath333
  • mathmath333
Probablity question
Mathematics
  • Stacey Warren - Expert brainly.com
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chestercat
  • chestercat
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
mathmath333
  • 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’.
anonymous
  • anonymous
http://clay6.com/qa/10684/one-card-is-drawn-at-random-from-a-well-shuffled-deck-of-52-cards-in-which-
triciaal
  • triciaal
|dw:1439916492853:dw|

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mathmath333
  • mathmath333
how do i calculate \(P(K\cap Q)\)
mathmath333
  • mathmath333
P(K\(\cup\)Q)=P(K)+P(Q)-P(K\(\cap\)Q)
triciaal
  • triciaal
first let me remind you I am not the best stats person
triciaal
  • triciaal
|dw:1439917813910:dw|
anonymous
  • anonymous
Events are independent if one does not affect the other.
freckles
  • 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: \[P((\text{Q} \text{ or } K) \text{ and } (\text{Q} \text{ or } \text{J}))=P(\text{Q} \text{ or } \text{K}) \cdot P(\text{Q} \text{ or } \text{J}) \\ \\ \text{ we know the left hand side just equals } P(\text{Q}) \\ \\ \text{ and we know } P(\text{Q})=\frac{4}{52}=\frac{1}{13} \\ \text{ so check to see if the right hand side is also } \frac{1}{13}\]
freckles
  • freckles
you should see it is not by what was worked out above
freckles
  • 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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