If the probability of being hospitalized during a year is 0.15 find the probability that no one in the family of 4 will be hospi
1 answer:
The probability that no one in the family of 4 will be hospitalized during a year is 0.52
Step-by-step explanation:
The probability for a person to be hospitalized during one year is
As a consequence, the probability for a person of NOT being hospitalized during one year is
If we have 4 people in the family, the probability of each of them of NOT being hospitalized during the year is independent from the probability of the others - therefore, these are independent events. This means that the total probability of the 4 people of not being hospitalized during a year is:
So, the probability that no one in the family of 4 will be hospitalized during a year is 0.52.
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All the numbers in the first equation have a common factor of 2. Removing that gives
.. x +4y = 6
making it easy to solve for x
.. x = 6 -4y
My choice would be to solve for x using the first equation.
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On second thought, it might actually be easier to solve either equation for 8y. That term then directly substitutes into the other equation (equivalent to adding the two equations).
.. 8y = 3x -11 . . . . . from the second equation
.. 2x +(3x -11) = 12 . . . substituting into the first equation
.. 5x = 23 . . . . . . . . . . collect terms, add 11 (what you would get by adding the equations in the first place)
.. x = 4.6
.. y = (3*4.6 -11)/8 = 0.35
.. x +4y = 6
making it easy to solve for x
.. x = 6 -4y
My choice would be to solve for x using the first equation.
_____
On second thought, it might actually be easier to solve either equation for 8y. That term then directly substitutes into the other equation (equivalent to adding the two equations).
.. 8y = 3x -11 . . . . . from the second equation
.. 2x +(3x -11) = 12 . . . substituting into the first equation
.. 5x = 23 . . . . . . . . . . collect terms, add 11 (what you would get by adding the equations in the first place)
.. x = 4.6
.. y = (3*4.6 -11)/8 = 0.35
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Step-by-step explanation:
