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?

Answer:0.667Step-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         0.05Now, 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] orP ( 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] orP ( less than 5 items sold | 3 or more items sold ) = [tex]\frac{\textup{0.2}}{\textup{0.3}}[/tex] orP ( less than 5 items sold | 3 or more items sold ) = 0.667