Category: Probability

What is the Probability that Selected Coin was Two-Headed?

Problem 739

There are three coins in a box. The first coin is two-headed. The second one is a fair coin. The third one is a biased coin that comes up heads $75\%$ of the time. When one of the three coins was picked at random from the box and tossed, it landed heads.

What is the probability that the selected coin was the two-headed coin?

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If a Smartphone is Defective, Which Factory Made It?

Problem 738

A certain model of smartphone is manufactured by three factories A, B, and C. Factories A, B, and C produce $60\%$, $25\%$, and $15\%$ of the smartphones, respectively. Suppose that their defective rates are $5\%$, $2\%$, and $7\%$, respectively.

If a smartphone of this model is found out to be detective, what is the probability that this smartphone was manufactured in factory C?

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Probability of Having Lung Cancer For Smokers

Problem 736

Let $C$ be the event that a randomly chosen person has lung cancer. Let $S$ be the event of a person being a smoker.
Suppose that 10% of the population has lung cancer and 20% of the population are smokers. Also, suppose that we know that 70% of all people who have lung cancer are smokers.

Then determine the probability of a person having lung cancer given that the person is a smoker.

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Overall Fraction of Defective Smartphones of Three Factories

Problem 735

A certain model of smartphone is manufactured by three factories A, B, and C. Factories A, B, and C produce $60\%$, $25\%$, and $15\%$ of the smartphones, respectively.

Suppose that their defective rates are $5\%$, $2\%$, and $7\%$, respectively. Determine the overall fraction of defective smartphones of this model.

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Jewelry Company Quality Test Failure Probability

Problem 731

A jewelry company requires for its products to pass three tests before they are sold at stores. For gold rings, 90 % passes the first test, 85 % passes the second test, and 80 % passes the third test. If a product fails any test, the product is thrown away and it will not take the subsequent tests. If a gold ring failed to pass one of the tests, what is the probability that it failed the second test?

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Probability Problems about Two Dice

Problem 727

Two fair and distinguishable six-sided dice are rolled.

(1) What is the probability that the sum of the upturned faces will equal $5$?

(2) What is the probability that the outcome of the second die is strictly greater than the first die?

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