Probability

Discrete Probability

Probability - Rule of Sum

         

Let XX be the number of televisions for a household chosen randomly. It is given that

P(X=1)=0.18,P(X=2)=0.36,P(X=3)=0.34,P(X=4)=0.08,P(X=5)=0.04. \begin{aligned} P(X=1) & = 0.18, \\ P(X=2) & = 0.36, \\ P(X=3) & = 0.34, \\ P(X=4) & = 0.08, \\ P(X=5) & = 0.04. \end{aligned}

If P(X<5)=aP(X < 5) = a, what is the value of 100a100a?

If a 20-sided fair die with sides distinctly numbered 1 through 20 is rolled, the probability that the answer is a perfect square can be expressed as ab\frac{a}{b} where aa and bb are coprime positive integers. What is the value of a+ba + b?

In a health examination of the 7272 employees at Acme Corporation, the numbers of employees with blood type AA and BB were 1111 and 19 19, respectively, and the remaining employees have blood type OO. If one of the 7272 employees is selected uniformly at random, the probability that the person's blood type is AA or BB can be expressed as ab\frac{a}{b}, where aa and bb are coprime positive integers. What is a+b?a+b?

Raoul chooses an integer uniformly at random from 11 to 34.34. The probability that his number is 66 or 3232 can be expressed as ab\frac{a}{b}, where aa and bb are coprime positive integers. What is the value of a+b?a+b?

In a group of 120120 students, 77 have black hair, 3535 have blond hair, 1212 have red hair, and the remaining have brown hair. If a student is selected uniformly at random from the group, the probability that the student has black hair or blond hair can be expressed as ab\frac{a}{b}, where aa and bb are coprime positive integers. What is the value of a+b?a+b?

Details and assumptions

Each student has exactly one hair color.

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