Question

a die is rolled 200 times with the following results.

outcome	1	2	3	4	5	6
frequency	32	36	44	20	30	38

what is the theoretical probability of the given event?
p(a number less than 5)
a. \\(\frac{1}{3}\\) b. \\(\frac{1}{2}\\) c. \\(\frac{2}{3}\\) d. \\(\frac{4}{7}\\)

Explanation:

Step1: Identify favorable outcomes

Numbers less than 5 on a die are 1, 2, 3, 4. So there are 4 favorable outcomes.

Step2: Total possible outcomes

A die has 6 possible outcomes (1, 2, 3, 4, 5, 6).

Step3: Calculate theoretical probability

Theoretical probability \( P = \frac{\text{Number of favorable outcomes}}{\text{Total number of possible outcomes}} = \frac{4}{6} = \frac{2}{3} \).

Answer:

C. \(\frac{2}{3}\)