The Mystery of the Lost Treasure

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A treasure hunter discovers a mysterious ancient box with two compartments. Each compartment contains a mix of gold and silver coins. The first compartment has 3 gold and 7 silver coins, while the second compartment has 8 gold and 2 silver coins. The treasure hunter decides to randomly select one coin from each compartment.

What is the probability that both coins selected are gold? Remember to use the principles of probability to calculate the likelihood of each event occurring independently and then combine them to find the total probability.

Comments

  1. AnonymousDecember 1, 2023 at 2:43 AM

    To solve "The Mystery of the Lost Treasure," we need to calculate the probability of selecting a gold coin from each compartment independently and then multiply these probabilities to find the total probability of both selections being gold coins.

    Probability of Selecting a Gold Coin from the First Compartment:

    The first compartment has 3 gold and 7 silver coins, making a total of 10 coins.
    The probability of selecting a gold coin from the first compartment is the number of gold coins divided by the total number of coins, which is 3/10.
    Probability of Selecting a Gold Coin from the Second Compartment:

    The second compartment has 8 gold and 2 silver coins, making a total of 10 coins.
    The probability of selecting a gold coin from the second compartment is the number of gold coins divided by the total number of coins, which is 8/10 or 4/5.
    Calculating the Total Probability:

    The events of selecting a coin from each compartment are independent.
    Therefore, the total probability of selecting gold coins from both compartments is the product of the individual probabilities.
    Total probability = Probability from the first compartment x Probability from the second compartment = 3/10 x 4/5.
    Calculating this, the total probability of selecting gold coins from both compartments is 3/10 x 4/5. You can simplify this to get the final answer.

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