أخواني ... أخواتي .... الأعزاء ..
في هذا المنتدى الرائع السلام عليكم ورحمه الله وبركاته ...

وبعد :

أشكركم جزيل الشكر على ماتقومون به من جهود مميزة ورائعة لخدمة إخوانكم في مجال الرياضيات في هذا المنتدى ...

ونظرأ لأني ادرس مادة الاحتمالات واجهت العديد من المشاكل في هذه المادة في بعض الأسئلة ...

لذا أرجو من الجميع قراءة هذة الأسئلة بتمعن وإفادتي فيها إما بحل أو فكرة ولكم جزيل الشكر ..

الأسئلة :


1. Given that the roll of a pair of fair dice yields a sum at least 5, what is the probability that the sum is exactly 7?

2. We select at random m objects from a set S of n objects and we denote by Am the set of the selected objects. What is the probability, p, that a particular element 0 of S is in Am? Justify your answer.

3. The game of “odd man out” is played with 3 people, each flipping a single coin.
All 3 flip their coin simultaneously; if one face is different from the other two, its owner is the odd man and he loses.
(a) What is the probability that there is an odd man on a given turn, assuming all three coins
are fair?

(b) If there is no odd man on the first turn, the coins are all flipped again, until the odd man is determined. What is the probability that an even number of turns is required to
determine the loser?

4. A code word contains five digits, each either 0 or 1; to be valid the word must contain exactly three 1’s and two 0’s. One word is selected at random from the valid code
words.
(a) Define X1 to be the first (left most ) digit and let X2 be the second digit in the word selected. Derive the probability law for (X1;X2).

(b) Let X3 be the third digit in the code word described in part (a) above, andderive the probability law for (X1;X2;X3).

ولكم تحياتي ,,,,