Question

you pick a card at random. 1 2 3 4 what is p(greater than 1 or factor of 81)? write your answer as a percentage.

Explanation:

Step1: Find factors of 81

The factors of 81 are 1, 3, 9, 27, 81. Among the numbers 1, 2, 3, 4, the factors of 81 are 1 and 3.

Step2: Define events

Let A be the event of picking a number greater than 1, and B be the event of picking a factor of 81. The set of numbers greater than 1 is {2, 3, 4}, and the set of factors of 81 among the given numbers is {1, 3}.

Step3: Use the formula for P(A or B)

The formula for \(P(A\cup B)=P(A)+P(B)-P(A\cap B)\). The total number of cards is \(n = 4\). \(P(A)=\frac{3}{4}\), \(P(B)=\frac{2}{4}\), and \(A\cap B=\{3\}\), so \(P(A\cap B)=\frac{1}{4}\).

Step4: Calculate P(A or B)

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Step5: Convert to percentage

To convert the probability to a percentage, we multiply by 100. So \(1\times100 = 100\%\)

Answer:

100%