+-4 points My Notes Ask Your Teacher A box in a certain supply room contains six
ID: 3277387 • Letter: #
Question
+-4 points My Notes Ask Your Teacher A box in a certain supply room contains six 40-W lightbulbs, five 60-W bulbs, and four 75-W bulbs. Suppose that three bulbs are randomly selected. (Round your answers to four decimal places.) (a) What is the probability that exactly two of the selected bulbs are rated 75-w? (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 75-W bulb is found. What is the probability that it is necessary to examine at least six bulbs? Need Help? Read It Talk to a TutorExplanation / Answer
Total number of ways of selecting three bulbs out of 15 = 15C3 = 455
(a) The two 75-W bulbs can be selected in 4C2 = 6 ways.
The remaining bulb can be selected in 5+6 = 11 ways.
The number of ways to select the bulbs = 6*11 = 66.
Probability = 66 / 455 = 0.1451
(b) Three 40-W bulbs can come in 6C3 = 20 ways.
Three 60-W bulbs can come in 5C3 = 10 ways.
Three 75-W bulbs can come in 4C3 = 4 ways.
Altogether they can come in 20+10+4 = 34 ways.
Probability = 34 / 455 = 0.0747.
(c) The one 40-W bulb can be selected in 6 ways.
The one 60-W bulb can be selected in 5 ways.
The one 75-W bulb can be selected in 4 ways.
Number of ways to select the bulbs = 6*5*4 = 120
=> Probability = 120 / 455 = 0.2637
(d) The probability that a bulb selected is not 75-W = 11 / 15.
=> Probability that five bulbs selected are all not 75-W = (11/15)5
Thus the probabilty that atleast six bulbs need to be examined = (11/15)5 = 0.2121.
Related Questions
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.