A box contains four 40-W bulbs, five 60-W bulbs and six 75-W bulbs. If bulbs are selected one by one in random order without replacement, what is the probability that at least two bulbs must be selected to obtain one that is rated 75 W

Question

Mathematics

Charlize Davies

28 September, 09:00

A box contains four 40-W bulbs, five 60-W bulbs and six 75-W bulbs. If bulbs are selected one by one in random order without replacement, what is the probability that at least two bulbs must be selected to obtain one that is rated 75 W

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Answers (1)

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Camille Stanley · Answer 1

60%

Step-by-step explanation:

We have that there are 6 75-W bulbs, that is to say these are the favorable cases. The total cases would be the sum of all the bulbs that would be:

4 + 5 + 6 = 15

Therefore the probability of at least 1 75-W bulbs is:

6/15 = 0.4

Now we must find the probability of at least 2 75-W bulbs, which is like this:

P (examine at least two 75-W bulbs) = 1 - P (examine at most one 75-W bulbs)

Replacing:

P (examine at least two 75-W bulbs) = 1 - 0.4 = 0.6

It means that the probability of least two 75-W bulbs is 60%