Soal Discrete Random Variable and Binomial Distribution

 1. Delivery of the same 20 types of laptops to a particular shop containing 3 defective products. if a school buys 2 laptops from this store. Find the probability distribution for the number of defective laptops

2. Obtain the probaility distribution of the total score when three cubical dice are thrown simultaneously 

3. A cubical dice is biased so that the probability of an odd number is three times the probability of an even number. Find the probability of the score 

4. A fair die is rolled repeatedly until a six is obtained. Let X denote the number of rolls required. The conditional probability that X ≥ 6 given X > 3 equals . . . 

5. A game involve a player throwing a fair 6 sided die. The game ends when a 6 ir obtained or the die has been rolled three times. The player wisn the game if a 6 is obtained. If X deontes the number of throws not obtaining a 6 in the game, where X can take values of 0, 1, 2, 3 . Tabulate the probability distribution of X 

6. an unbiased dice is thrown and the result X is the score if it is 3 or more. If the score is 2 or less, the dice is thrown again and the result X is the sum of the score on the two throws. Find 

(a) P(X = 6) 

(b) P(X = 7) 

(c) E(X) 

(d) Given that the process is repeated 50 times and N is the number of occasions that a result of 7 is obtained, Find E(N) and Var(N) 

7. Probability that Paul Pogba scoring from the penalty are 80%. If he shoots 10 times then the chances of creating at least 3 goals are. . . . 

8. A fair coin is tossed 4 times. What is the probability of getting at least 2 tails? 

9. Joseph and four friends each have an independent probability 0.45 of winning prize. Find the probability that : (a) Exactly two of the five friends win a prize (b) Joseph and only one friend win a prize 

10. For X v B(10, 0.3) calculate P(µ − σ < X < µ + σ) 

11. There are n white balls and m black balls in an urn. In a sampling experiment , k balls are drawn at random with replacement after each ball is drawn and the random variabel X denotes the number of black balls drawn 

(a) Write down the distribution of X giving its parameter 

(b) Find an expression for the probability that at least one black ball is drawn 

(c) If the number of white balls is 9 times that of black balls, determine the least number of balls that must be drawn so that probability in (b) exceeds 1 2 

12. Coin A is tossed three times and coin B is tossed 4 times. Determine the probability that the number of Head that come from the toss of two coins is the same