Question

1. a financial planner has three portfolios: a, b, and c. because investors have different tolerances for risks, 35% of people are likely to invest in portfolio a, 25% are likely to invest in b, and 40% are likely to invest in c. each portfolio has both stocks and bonds, and investors are equally likely to choose either. this is a tree diagram that represents the probability of investors choosing the different financial products. tree diagram with branches labeled x, 0.25, 0.4 and sub - branches 0.5 each what is the value of x? options: 0.40, 0.50, 0.25, 0.35

Explanation:

Step1: Recall total probability rule

The sum of probabilities of all mutually exclusive and exhaustive events is 1. Here, the probabilities of choosing portfolios A, B, C (represented by \(X\), \(0.25\), \(0.4\)) should sum to 1.

Step2: Set up the equation

Let the probability of portfolio A be \(X\). Then \(X + 0.25+ 0.4=1\).

Step3: Solve for \(X\)

Simplify the equation: \(X + 0.65 = 1\). Subtract \(0.65\) from both sides: \(X=1 - 0.65 = 0.35\).

Answer:

\(0.35\)