Question
Download Solution PDFConsider a dice with the property that the probability of a face with n dots showing up is proportional to n. The probability of face showing 4 dots is
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFConcept:
The probability of occurrence of an event E, within a sample space S, is given by:
P(E) = n(E) / n(S)
where P(E) = probability of occurrence of the event E,
n(E) = number of times the event E occurs, and
n(S) = number of points in the sample space S.
In the case of two independent events, the probability of the first event does not affect the probability of the second event.
Calculation:
Given:
Probability of face on 1 dot ∝ 1
Probability of face on 2 dots ∝ 2
\(\vdots \)
Similarly, probability of face on 6 dots ∝ 6
Total number of = 1 + 2 + 3 + 4 + 5 + 6 = 21
Now, the probability of the face with 4 dots showing up is \(= \frac{4}{{21}}\)
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