Question

A financial adviser recommends a list of stocks for purchase and claims that 60% of stocks from the list increase in value. If a client randomly selects 4 stocks from the list, determine the probability that at least 2 of the stocks increase in value. Assume that the selection of the stocks are independent and that the number of stocks that increase in value has a binomial distribution.

Answer 1

To calculate the probability that at least two of the four stocks selected will increase in value, we use the binomial distribution formula to find the sum of the probabilities of two, three, and four stocks increasing in value given a 60% chance of each stock increasing.

Step-by-step explanation:

The question asks us to determine the probability that at least two of the four stocks selected from a recommended list will increase in value. Given the assertion that each stock has a 60% chance of increasing in value and assuming that the stocks are selected independently, we can model this using the binomial distribution. To find the probability of at least two stocks increasing in value, we calculate the sum of the probabilities of exactly two, three and four stocks increasing in value.

We use the binomial probability formula P(X = k) = (n choose k) * p^k * (1-p)^(n-k), where n is the number of trials (stocks selected), k is the number of successes (stocks increasing in value), and p is the probability of success (60% or 0.6 in this case).

To calculate:

• The probability of exactly two stocks increasing in value: (4 choose 2) * 0.6^2 * 0.4^2
• The probability of exactly three stocks increasing in value: (4 choose 3) * 0.6^3 * 0.4^1
• The probability of all four stocks increasing in value: (4 choose 4) * 0.6^4 * 0.4^0

We then sum these probabilities to get the total probability of at least two stocks increasing in value.