There are 250 light bulbs in the box, of which 100 are 90W, 50 are 60W, 50 are 25W and 50 are 15W

There are 250 light bulbs in the box, of which 100 are 90W, 50 are 60W, 50 are 25W and 50 are 15W. Determine the probability that the power of any random bulb taken will not exceed 60W.

1. We consider the following events:
A = {bulb power equal to 90W}, probability P (A) = 100/250 = 0.4;
B = {bulb power equal to 60W};
C = {bulb power equal to 25W};
D = {bulb power is 15W}.
2. Events A, B, C, D form a complete system, since they are all incompatible and one of them will necessarily occur in a given experiment (choosing a bulb). The probability of the onset of one of them is a reliable event, then P (A) + P (B) + P (C) + P (D) = 1.
3. Events {bulb power of not more than 60W} (ie less than or equal to 60W), and {bulb power of more than 60W} (in this case, 90W) are opposite. By the property of opposite numbers, P (B) + P (C) + P (D) = 1-P (A).
4. Given that P (B) + P (C) + P (D) = P (B + C + D), we obtain P (B + C + D) = 1-P (A) = 1-0, 4 = 0.6.

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