Investing is a game of chance. Suppose there is a 36% chance that a risky stock investment will end up in a total loss of your investment. Because the rewards are so high, you decide to invest in five independent risky stocks. Find the probability that at least one of your five investments becomes a total loss. Round to the nearest ten-thousandth when necessary.

Question

Mathematics

Ross Rosales

19 February, 11:21

Investing is a game of chance. Suppose there is a 36% chance that a risky stock investment will end up in a total loss of your investment. Because the rewards are so high, you decide to invest in five independent risky stocks. Find the probability that at least one of your five investments becomes a total loss. Round to the nearest ten-thousandth when necessary.

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Korbin Solis · Answer 1

Answer: P (x ≥ 1) = 0.893

Step-by-step explanation:

We would assume a binomial distribution for the outcome of the investment. The formula is expressed as

P (x = r) = nCr * p^r * q^ (n - r)

Where

x represent the number of successes.

p represents the probability of success.

q = (1 - r) represents the probability of failure.

n represents the number of trials or sample.

From the information given,

p = 36% = 36/100 = 0.36

q = 1 - p = 1 - 0.36

q = 0.64

n = 5

Therefore,

P (x ≥ 1) = 1 - P (x = 0)

P (x = 0) = 5C0 * 0.36^0 * 0.64^ (5 - 0)

P (x = 0) = 1 * 1 * 0.107

P (x = 0) = 0.107

P (x ≥ 1) = 1 - 0.107 = 0.893