Rolling a dice three times, evaluate the probability of having at least one 6. (5 marks)
Drawn a card from a deck of 52 cards, verify whether the following events are statistically independent:
a) A = {drawing of a picture card}; B ={drawing of a hearth card}
b) What if the king of hearths is missing from the deck of cards?
c) What if a card, at random, is missing? (5 marks)
d) if a card is drawn at random from a deck of cards. Find the probability of getting the King of hearts.
1.
2.
a)
"P(A)=\\dfrac{12}{52}=\\dfrac{3}{13}""P(B)=\\dfrac{13}{52}=\\dfrac{1}{4}"
"P(A\\cap B)=\\dfrac{3}{52}"
"P(A)P(B)=\\dfrac{3}{13}(\\dfrac{1}{4})=\\dfrac{3}{52}=P(A\\cap B)"
The events "A" and "B" are statistically independent.
b)
"P(B)=\\dfrac{12}{51}=\\dfrac{4}{17}"
"P(A\\cap B)=\\dfrac{3}{51}=\\dfrac{1}{17}"
"P(A)P(B)=\\dfrac{11}{51}(\\dfrac{4}{17})=\\dfrac{44}{867}\\not=\\dfrac{1}{17}=P(A\\cap B)"
The events "A" and "B" are not statistically independent.
c)
i) The missing card is neither heart nor picture.
"P(B)=\\dfrac{13}{51}"
"P(A\\cap B)=\\dfrac{4}{51}"
"P(A)P(B)=\\dfrac{4}{17}(\\dfrac{13}{51})=\\dfrac{52}{867}\\not=\\dfrac{4}{51}=P(A\\cap B)"
The events "A" and "B" are not statistically independent.
ii) The missing card is picture but is not heart
"P(B)=\\dfrac{13}{51}"
"P(A\\cap B)=\\dfrac{4}{51}"
"P(A)P(B)=\\dfrac{11}{51}(\\dfrac{13}{51})=\\dfrac{143}{2601}\\not=\\dfrac{4}{51}=P(A\\cap B)"
The events "A" and "B" are not statistically independent.
iii) The missing card is heart but is not picture
"P(B)=\\dfrac{12}{51}=\\dfrac{4}{17}"
"P(A\\cap B)=\\dfrac{4}{51}"
"P(A)P(B)=\\dfrac{4}{17}(\\dfrac{4}{17})=\\dfrac{16}{289}\\not=\\dfrac{4}{51}=P(A\\cap B)"
The events "A" and "B" are not statistically independent.
iv) The missing card is heart and is picture
"P(B)=\\dfrac{12}{51}=\\dfrac{4}{17}"
"P(A\\cap B)=\\dfrac{3}{51}=\\dfrac{1}{17}"
"P(A)P(B)=\\dfrac{11}{51}(\\dfrac{4}{17})=\\dfrac{44}{867}\\not=\\dfrac{1}{17}=P(A\\cap B)"
The events "A" and "B" are not statistically independent.
d)
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