Question

you pick a card at random. 6 7 8 9 what is p(greater than 7 or factor of 60)? write your answer as a percentage rounded to the nearest tenth.

Explanation:

Step1: Identify numbers greater than 7

The numbers greater than 7 in the set {6, 7, 8, 9} are 8 and 9.

Step2: Identify factors of 60

The factors of 60 are 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60. In the set {6, 7, 8, 9}, the factor of 60 is 6.

Step3: Use the formula for the probability of the union of two events

The formula for \(P(A\cup B)=P(A)+P(B)-P(A\cap B)\). Here, \(A\) is the event of picking a number greater than 7 and \(B\) is the event of picking a factor of 60. The total number of cards \(n = 4\). \(P(A)=\frac{2}{4}\), \(P(B)=\frac{1}{4}\), and \(A\cap B=\varnothing\) (no common - elements), so \(P(A\cap B) = 0\). Then \(P(A\cup B)=\frac{2 + 1}{4}=\frac{3}{4}\).

Step4: Convert to percentage

To convert \(\frac{3}{4}\) to a percentage, we calculate \(\frac{3}{4}\times100\%=75.0\%\)

Answer:

75.0%