Question

A spinner of a board game can land on any one of three regions​labeled: A,​ B, and C. If the probability the spinner lands on B is

three times that of A, and the probability the spinner lands on C is

five times that of ​A, find the probability the spinner lands on A.

Round to 4 decimal places.

Answer 1

Answer:

The probability of the spinner landing on A is 0.1111.

Step-by-step explanation:

The possible outcomes of a board game is that it can lead on any three of the regions, A, B and C.

The probability of all the outcomes of an event sums up to be 1.

$P(E) = P(E_{1})+P(E_{2})+...+P(E_{n})=1$

According to the provided information:

P (B) = 3 P (A)

P (C) = 5 P (A)

Compute the probability of the spinner landing on A as follows:

$P(A)+P(B)+P(C)=1\\P(A)+3P(A)+5P(A)=1\\9P(A)=1\\P(A)=\frac{1}{9}\\=0.111111\\\approx0.1111$

Thus, the probability of the spinner landing on A is 0.1111.