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Wewaii [24]
3 years ago
15

Two candidates are randomly selected. a. List all the possible outcomes. b. What is the probability that both are qualified? c.

What is the probability that exactly one is qualified?
Mathematics
1 answer:
steposvetlana [31]3 years ago
5 0

Question:

Four candidates are to be interviewed for a job. Two of them, numbered 1 and 2, are qualified, and the other two, numbered 3 and 4, are not.

Answer:

a. S = {12,13,14,23,24,34}

b. 1/6

c. ⅔

Step-by-step explanation:

Let S = Sample Space i.e. total possible outcomes

Given that candidates 1 and 2 are qualified and 3 and 4 are not qualified.

If two candidates are randomly selected. The list of all possible outcomes is as follows

S:{12,13,14,23,24,34}

And the number of outcomes is 6

b. What is the probability that both are qualified?

The event that both are qualified is given as {12} or {21}

From the sample space in (a) above, there's only one occurrence of {12} = 1

So, the probability is calculated as 1/6

c. What is the probability that exactly one is qualified?

The event that one one is qualified is given as {13,14,23,24}

Total = 4

Probability = 4/6

Probability = ⅔

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Complete question :

Members of the swim team want to wash their hair. The bathroom has less than 5600 liters of water and at most 2.5 liters of shampoo. 70L+ 60S < 5600 represents the number of long-haired members L and short-haired members S who can wash their hair with less than 5600 liters of water. 0.02L + 0.01S < or equal to 2.5 represents the number of long-haired members and short-haired members who can wash their hair with at most 2.5 liters of shampoo. Does the bathroom have enough water and shampoo for 8 long-haired members and 7 short -haired members?

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Step-by-step explanation:

Given that:

Number of long and short hair member who can wash their hair with less than 5600 litres of water.

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To check if bathroom has enough water and shampoo for 8 long haired and 7 short haired members.

Water check:

70L+ 60S < 5600

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Inequality constraint is satisfied ; There is enough water.

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0.02L + 0.01S ≤ 2.5

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