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The random variable X, representing the number of items sold in a week, has the following probability distribution: x 0 1 2 3 4 5 6 P(X = x) 0.10 0.20 0.40 0.15 0.05 0.05 0.05 By the fourth day of a particular week, 3 items have already sold. What is the probability that there will be less than a total of 5 items sold during that week?

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Respuesta :

Answer:

0.667

Step-by-step explanation:

Data provided:

x                0                1              2              3              4              5              6

P(X = x)    0.10         0.20         0.40         0.15         0.05         0.05         0.05

Now,

The probability that less than 5 items will be sold in a week given that 3 items have already been sold can be calculated as;

P ( less than 5 items sold | 3 or more items sold )

= [tex]\frac{\textup{ 3 or more and less than 5 items sold}}{\textup{3 or more items sold}}[/tex]

= [tex]\frac{\textup{3 or 4 items sold}}{\textup{3 or more items sold}}[/tex]

or

P ( less than 5 items sold | 3 or more items sold ) = [tex]\frac{\textup{0.15 + 0.05}}{\textup{0.15 + 0.05 + 0.05 + 0.05}}[/tex]

or

P ( less than 5 items sold | 3 or more items sold ) = [tex]\frac{\textup{0.2}}{\textup{0.3}}[/tex]

or

P ( less than 5 items sold | 3 or more items sold ) = 0.667

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