2018-09-30 23:01:58 +01:00 
										
									 
								 
							 
							
								
							 
							
								 
							
							
								---
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							
							
								id: 5900f4a01000cf542c50ffb2
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							
							
								title: 'Problem 307: Chip Defects'
							 
						 
					
						
							
								
									
										
										
										
											2020-11-27 19:02:05 +01:00 
										
									 
								 
							 
							
								
									
										 
								
							 
							
								 
							
							
								challengeType: 5
							 
						 
					
						
							
								
									
										
										
										
											2019-08-05 09:17:33 -07:00 
										
									 
								 
							 
							
								
									
										 
								
							 
							
								 
							
							
								forumTopicId: 301961
							 
						 
					
						
							
								
									
										
										
										
											2021-01-13 03:31:00 +01:00 
										
									 
								 
							 
							
								
									
										 
								
							 
							
								 
							
							
								dashedName: problem-307-chip-defects
							 
						 
					
						
							
								
									
										
										
										
											2018-09-30 23:01:58 +01:00 
										
									 
								 
							 
							
								
							 
							
								 
							
							
								---
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							
							
								
							 
						 
					
						
							
								
									
										
										
										
											2020-11-27 19:02:05 +01:00 
										
									 
								 
							 
							
								
									
										 
								
							 
							
								 
							
							
								# --description--
  
						 
					
						
							
								
									
										
										
										
											2018-09-30 23:01:58 +01:00 
										
									 
								 
							 
							
								
							 
							
								 
							
							
								
							 
						 
					
						
							
								
									
										
										
										
											2020-11-27 19:02:05 +01:00 
										
									 
								 
							 
							
								
									
										 
								
							 
							
								 
							
							
								k defects are randomly distributed amongst n integrated-circuit chips produced by a factory (any number of defects may be found on a chip and each defect is independent of the other defects).
							 
						 
					
						
							
								
									
										
										
										
											2018-09-30 23:01:58 +01:00 
										
									 
								 
							 
							
								
							 
							
								 
							
							
								
							 
						 
					
						
							
								
									
										
										
										
											2020-11-27 19:02:05 +01:00 
										
									 
								 
							 
							
								
									
										 
								
							 
							
								 
							
							
								Let p(k,n) represent the probability that there is a chip with at least 3 defects. For instance p(3,7) ≈ 0.0204081633.
							 
						 
					
						
							
								
									
										
										
										
											2018-09-30 23:01:58 +01:00 
										
									 
								 
							 
							
								
							 
							
								 
							
							
								
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							
							
								Find p(20 000, 1 000 000) and give your answer rounded to 10 decimal places in the form 0.abcdefghij
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							
							
								
							 
						 
					
						
							
								
									
										
										
										
											2020-11-27 19:02:05 +01:00 
										
									 
								 
							 
							
								
									
										 
								
							 
							
								 
							
							
								# --hints--
  
						 
					
						
							
								
									
										
										
										
											2018-09-30 23:01:58 +01:00 
										
									 
								 
							 
							
								
							 
							
								 
							
							
								
							 
						 
					
						
							
								
									
										
										
										
											2020-11-27 19:02:05 +01:00 
										
									 
								 
							 
							
								
									
										 
								
							 
							
								 
							
							
								`euler307()`  should return 0.7311720251. 
						 
					
						
							
								
									
										
										
										
											2018-09-30 23:01:58 +01:00 
										
									 
								 
							 
							
								
							 
							
								 
							
							
								
							 
						 
					
						
							
								
									
										
										
										
											2020-11-27 19:02:05 +01:00 
										
									 
								 
							 
							
								
									
										 
								
							 
							
								 
							
							
								```js
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							
							
								assert.strictEqual(euler307(), 0.7311720251);
							 
						 
					
						
							
								
									
										
										
										
											2018-09-30 23:01:58 +01:00 
										
									 
								 
							 
							
								
							 
							
								 
							
							
								```
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							
							
								
							 
						 
					
						
							
								
									
										
										
										
											2020-11-27 19:02:05 +01:00 
										
									 
								 
							 
							
								
									
										 
								
							 
							
								 
							
							
								# --seed--
  
						 
					
						
							
								
									
										
										
										
											2018-09-30 23:01:58 +01:00 
										
									 
								 
							 
							
								
							 
							
								 
							
							
								
							 
						 
					
						
							
								
									
										
										
										
											2020-11-27 19:02:05 +01:00 
										
									 
								 
							 
							
								
									
										 
								
							 
							
								 
							
							
								## --seed-contents--
  
						 
					
						
							
								
									
										
										
										
											2018-09-30 23:01:58 +01:00 
										
									 
								 
							 
							
								
							 
							
								 
							
							
								
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							
							
								```js
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							
							
								function euler307() {
							 
						 
					
						
							
								
									
										
										
										
											2020-09-15 09:57:40 -07:00 
										
									 
								 
							 
							
								
									
										 
								
							 
							
								 
							
							
								
							 
						 
					
						
							
								
									
										
										
										
											2018-09-30 23:01:58 +01:00 
										
									 
								 
							 
							
								
							 
							
								 
							
							
								  return true;
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							
							
								}
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							
							
								
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							
							
								euler307();
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							
							
								```
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							
							
								
							 
						 
					
						
							
								
									
										
										
										
											2020-11-27 19:02:05 +01:00 
										
									 
								 
							 
							
								
									
										 
								
							 
							
								 
							
							
								# --solutions--
  
						 
					
						
							
								
									
										
										
										
											2018-09-30 23:01:58 +01:00 
										
									 
								 
							 
							
								
							 
							
								 
							
							
								
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							
							
								```js
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							
							
								// solution required
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							
							
								```