A box in a certain supply room contains four 40w, five 60w, and six 75w light-bulbs. suppose that three bulbs are randomly selec
ted. a.what is the probability that exactly two of the selected bulbs are rated 75w?
b.what is the probability that all three of the selected bulbs have the same rating?
c.what is the probability that one bulb of each type is selected?
d.suppose, now, that bulbs are to be selected one by one until a 75w bulb is found. what is the probability that it is necessary to examine at least six bulbs?
Situation satisfies the criteria for the use of hypergeometric distribution. Since no replacement is made, binomial distribution is not applicable (probability does not remain constant).
A=number of target wattage bulbs B=number of non-targeted wattage bulbs a=number of target wattage bulbs selected b=number of non-targeted wattage bulbs selected
P(a,b)=C(A,a)*C(B,b)/C(A+B,a+b) where C(n,x)=combination of x items chosen from n=n!/(x!(n-x)!)
For all following problems, A+B=4+5+6=15 a+b=3 (selected)
(b) target wattage = each of the three Probability = sum of probabilities of choosing 3 40,60,75-watt bulbs P(3x40W)+P(3x60W)+P(3x75W) Case (A,B,a,b) 3x40W (4,11,3,0) 3x60W (5,10,3,0) 3x75W(6,9,3,0)
Since the direction is not specified, it can be safe to assume that the direction of rotation is counterclockwise.
300 degrees is 60 degrees less than 360 degrees, which is a full rotation. Thus, 300 degrees counterclockwise is the same as 60 degrees clockwise.
Note that this shape is a hexagon. Thus, we can divide a hexagon into 6 equilateral triangles, each with measures of 60 degrees. Just move OQ to the adjacent clockwise equilateral triangle and see what it overlaps with.
OQ is the altitude of the equilateral triangle, so our answer will be the altitude of the adjacent clockwise equilateral triangle.