# Question: Suppose that a die has n sides numbered i

Suppose that a die has n sides numbered i = 1, 2,···, n. Assume that the probability of it coming up on the side numbered i is the same for each value of i. The die is rolled n times (assume independence) And a “ match” is defined to be the occurrence of side i on the ith roll. Prove that the probability of at least one match is given by

**View Solution:**## Answer to relevant Questions

Show that P(A ∪ B) ≥ 1- P(A') - P(B') for Any two events A And B defined in the sample space S. If Ms. Brown buys one of the houses advertised for sale in a Seattle newspaper (on a given Sunday) , T is the event that the house has three or more baths, U is the event that it has a fireplace, V is the event that it costs ...In Figure 2.14, E, T, And N are the events that a car brought to a garage needs an engine overhaul, trans-mission repairs, or new tires. Express in words the events represented by (a) Region 1; (b) Region 3; (c) Region 7; ...The probabilities that the serviceability of a new X-ray machine will be rated very difficult, difficult, aver-age, easy, or very easy are, respectively, 0.12, 0.17, 0.34, 0.29, And 0.08. Find the probabilities that the ...Among the 78 doctors on the staff of a hospital, 64 carry malpractice insurance, 36 are surgeons, And 34 of the surgeons carry malpractice insurance. If one of these doctors is chosen by lot to represent the hospital staff ...Post your question