The secret number has 5 digits: 3, 9, 1, 6, 2
2 answers:
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PART 1.
Out of the 6 numbers of the board, there are 2 pairs whose product is 12: 6 and 2, and 4 and 3.
Notice that you could spin, for instance, a 6 first and then a 2. Or you could also spin a 2 first and then a 6. This tells us that each pair of numbers can be spun in two different ways. This gives us a total of 4 possible combinations whose product is 12:
Now, let's calculate the number of possible combinations. Notice that, for example, you can spin a 1 and then a 1, 2, 3, 4, 5 or 6. This will give us 6 possible combinations for number 1:
This will also happen for each of the 6 numbers on the board. If each number gives us 6 combinations, and there are 6 numbers, the total number of combinations will be:
Now, we take the number of favorable outcomes (the pairs whose product is 12) and divide it by the total number of outcomes:
This way, we can conclude that the probability that the product of the numbers spun is 12 is 1/9.
PART 2.
Number 3 is one of the 10 numbers given (0,1,2,3,4,5,6,7,8,9). This way, the probability of choosing number 3 is:
Now, out of all the 4 letters given (A,B,C,D), 3 are consonants. This way, the probability of choosing a consonant is:
This way, the probability of chosing number 3 and a consonant is:
This way, we can conclude that the probability that the number 3 and a consonant are selected is 3/40