Chapter 13.6, Problem 12CFU

To determine

The solution of the probability.

Answer to Problem 12CFU

  $0.1372$ .

Explanation of Solution

Given information:

A stock broker is researching $13$ independent stocks. An investment in each will either make or lose money. The probability that each stock will make money is $\frac{5}{8}$ . What is the probability that exactly $10$ of the stocks will make money.

Calculation:

From the given information, stock broker is researching $13$ independent stocks and the probability that each stock will make money is $\frac{5}{8}$ are as shown below:

  $P($ Stock makes money $)$$=\frac{5}{8}$

  $P($ Stock loses money $)$$=\frac{3}{8}$

Now, the probability that exactly $10$ of the stocks will make money:

  $P(10$ Stocks make money $)=C(13,10){\left(\frac{5}{8}\right)}^{10}{\left(\frac{3}{8}\right)}^3\approx 0.1372$

Thus, the solution of the probability is $0.1372$ .