Thank you sir. Many people get the following question wrong, so please explain. [Question] Find the probabilities that the following events will occur when two dice are rolled. ①Both show odd numbers ②One shows odd number and another shows evenn number ③Both show even number P(E):the probability that event E occurs. 【Distinguishable dice A and B】 (the number that dice A shows,the number dice B shows):event If we only judge whether the numbers indicated by the dice are odd or even, the following four events will occur. (odd,odd) (odd,even) (even,odd) (even,even) If each event occurs with equal probability, the probability is 1/4. Therefore, P(①)=1/4, P(②)=1/2, P(③)=1/4 (1) If we judge the number(1,2,···,6) indicated by the dice ,the following 36 events will occur. (1,1), (1,3),(1,5) (1,2),(1,4),(1,6) (3,1), (3,3),(3,5) (3,2),(3,4),(3,6) (5,1), (5,3),(5,5) (5,2),(5,4),(5,6) (2,1), (2,3),(2,5) (2,2),(2,4),(2,6) (4,1), (4,3),(4,5) (4,2),(4,4),(4,6) (6,1), (6,3),(6,5) (6,2),(6,4),(6,6) If each event occurs with equal probability, the probability is 1/36. Therfore P(①)=9×(1/36)=1/4, P(②)=18×(1/36)=1/2, P(③)=9×(1/36)=1/4 (2) (2) matches (1). 【Indistinguishable two dice】 (odd,even)is the same event as(even,odd). Thererore, if we only judge whether the numbers indicated by the dice are odd or even, the following three events will occur. (odd,odd) (even,odd) (even,even) If each event occurs with equal probability, the probability is 1/3. Therefore P(①)=1/3, P(②)=1/3, P(③)=1/3 (3) (1,3) is the same event as (3,1). If we judge the number(1,2,···,6) indicated by the dice ,the following 21 events will occur. (1,1) (3,1), (3,3) (5,1), (5,3),(5,5) (2,1), (2,3),(2,5) (2,2) (4,1), (4,3),(4,5) (4,2),(4,4) (6,1), (6,3),(6,5) (6,2),(6,4),(6,6) If each event occurs with equal probability, the probability is 1/21. Therefore P(①)=6×(1/21)=2/7, P(②)=9×(1/21)=3/7, P(③)=6×(1/21)=2/7 (4) (4) contradicts (3).
super, i need a solution for this problem, a pair of dice rolled once. let x be the random variable whose value for any out come is the sum of the two numbers on the dice, find P(3
I don't know why it bothered me so badly that you didn't reduce 15/36, while the other ratios got that reduction love. I guess I am just easily bothered by unimportant things. Thanks for the video!
Thanks for pointing that out. I should have reduced it to 5/12 as has been done for the others. I highly appreciate and will incorporate the correction in the video also. Thanks
As you can see in the table created for the sum there are 6 ways the sum of two dice can be 7 There are in all 36 ways of adding numbers of two dice Probability is ratio of Favourable and Total. Probability can never be more than 1. Hope that helps. Thanks
Thanks for the request. Here is an example with 3 dice: ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-gWJDSzsJhq4.html You can search my videos by Anil Kumar Topic example , anil kumar three dics Thanks
Lowest probability will be Zero and the Highest will be 1 (100%). Sum less than 1 will give the lowest probability and Sum greater than 1 will be highest.
You made a mistake? You totally left out the probability of rolling a 6???? WHY????????????? Didn't you mean Probability of rolling a dice with a value of LESS THAN 7????????????