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bag of coins contains two quarters 5 dimes 3 nickels and 4 pennies if two coins are randomly chosen from the bag one after the other not replaced and if the total value of the chosen coins is $0.26 what is the probability that a third coin randomly chosen from the back will be a penny

Respuesta :

konrad509
A - the total value of the first two chosen coins is $0.26
B - third chosen coin is a penny

[tex]P(B|A)=\dfrac{P(A \cap B)}{P(A)}\\\\ |\Omega|=14\cdot13=182\\ |A|=2\cdot4\cdot2!=16\\ |A \cap B|=16\cdot3=48\\\\ P(A \cap B)=\dfrac{48}{182\cdot12}=\dfrac{2}{91}\\ P(A)=\dfrac{16}{182}=\dfrac{8}{91}\\\\ P(B|A)=\dfrac{\dfrac{2}{91}}{\dfrac{8}{91}}=\dfrac{2}{91}\cdot\dfrac{91}{8}=\dfrac{1}{4} [/tex]



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