5. These two questions are problems tha t pertain to sample spaces with equally
ID: 3148348 • Letter: 5
Question
5. These two questions are problems tha t pertain to sample spaces with equally likely outcomes. (a) (10 points) A factory produces fuses, which are packaged in boxes of 10. Three fuses are selected at random from each box for inspection. The box is rejected if at least one of these three fuses is defective. What is the probability that a box containing five defective fuses will be rejected? %) 720 [2 2 o.lolo (b) (10 points) Three people are chosen at random. What is the probability that at least two of them were born on the same day of the week?Explanation / Answer
(a) Here the box contains 5 defective fuses. We reject the lot if atleast one of the fuse out of three is defective.
so, if in these 3 fuses, there comes one defective piece out of 5, we will reject the lot.
Pr(We will reject the lot) = 1 - Pr(There is no defective piece out of 3 sampled pieces)
= 1 - 5C0 * 5C3/ 10C3
= 1 - 10/120 = 11/12
(b) Here there are three people. we have to find that atleast two of them were born on any given day of week.
Pr(Two of them born on same day) = 1- Pr(Noone will share the same birthday in a week)
= 1 - 7/7 * 6/7 * 5/7 = 1 - 30/49 = 19/49
Here the first person have 7 days where his birthday can lie. THe second person can have birthday on any of the 6 days and the third one is on next 5 days.
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