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Mildred has a bag of coins. The bag contains 10 dimes, 5 nickels, and 1 penny. She will randomly select 2 coins form the bag one at a time without replacement. What is the probability that Mildred will select a dime first and then a penny? A. (83)/(120) B. (11)/(16) C. (5)/(128) D. (1)/(24)

Mildred has a bag of coins. The bag contains 1010 dimes, 55 nickels, and 11 penny. She will randomly select 22 coins form the bag one at a time without replacement. What is the probability that Mildred will select a dime first and then a penny?\newlineA. 83120 \frac{83}{120} \newlineB. 1116 \frac{11}{16} \newlineC. 5128 \frac{5}{128} \newlineD. 124 \frac{1}{24}

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Q. Mildred has a bag of coins. The bag contains 1010 dimes, 55 nickels, and 11 penny. She will randomly select 22 coins form the bag one at a time without replacement. What is the probability that Mildred will select a dime first and then a penny?\newlineA. 83120 \frac{83}{120} \newlineB. 1116 \frac{11}{16} \newlineC. 5128 \frac{5}{128} \newlineD. 124 \frac{1}{24}
  1. Determine total number of coins: Determine the total number of coins in the bag.\newlineMildred has 1010 dimes, 55 nickels, and 11 penny, so the total number of coins is 10+5+110 + 5 + 1.\newlineTotal number of coins = 1616.
  2. Calculate dime selection probability: Calculate the probability of selecting a dime first.\newlineSince there are 1010 dimes out of 1616 coins, the probability of selecting a dime first is 1016\frac{10}{16}.\newlineProbability of first dime = 1016\frac{10}{16}.
  3. Calculate penny selection probability: Calculate the probability of selecting a penny second, after a dime has been selected.\newlineAfter selecting a dime, there are now 1515 coins left in the bag, and only 11 of them is a penny.\newlineProbability of second penny = 115\frac{1}{15}.
  4. Calculate combined probability: Calculate the combined probability of both events happening in sequence (selecting a dime first and then a penny).\newlineTo find the combined probability, multiply the probability of the first event by the probability of the second event.\newlineCombined probability = (1016)×(115)(\frac{10}{16}) \times (\frac{1}{15}).
  5. Perform multiplication for combined probability: Perform the multiplication to find the combined probability.\newlineCombined probability = (1016)×(115)=10(16×15)=10240(\frac{10}{16}) \times (\frac{1}{15}) = \frac{10}{(16\times15)} = \frac{10}{240}.
  6. Simplify fraction for final probability: Simplify the fraction to find the final probability. \newline10240\frac{10}{240} can be simplified by dividing both the numerator and the denominator by 1010.\newlineFinal probability = 124\frac{1}{24}.

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