The diagram shows a security lock.You have to enter the correct code to open the lock. The correct code is B3Dan does not know the code.He enters at random one of the letters.He then enters at random one of the numbers.Work out the probability that Dan enters the correct code.
Question
The diagram shows a security lock.You have to enter the correct code to open the lock. The correct code is B3Dan does not know the code.He enters at random one of the letters.He then enters at random one of the numbers.Work out the probability that Dan enters the correct code.
Solution
The probability of an event is calculated by dividing the number of favorable outcomes by the total number of outcomes.
In this case, Dan has to guess a letter and a number.
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For the letter, if we assume that the lock uses the English alphabet, there are 26 possible letters that Dan could enter. Only one of these (B) is correct. So the probability that Dan correctly guesses the letter is 1/26.
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For the number, if we assume that the lock uses single digit numbers, there are 10 possible numbers (0-9) that Dan could enter. Only one of these (3) is correct. So the probability that Dan correctly guesses the number is 1/10.
Since Dan has to guess both the letter and the number correctly to enter the correct code, we multiply these probabilities together to get the overall probability.
So, the probability that Dan enters the correct code is (1/26) * (1/10) = 1/260.
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