Family Tree

Family Tree

About Me

My photo
Kathmandu, Bagmati Zone, Nepal
I am Basan Shrestha from Kathmandu, Nepal. I use the term 'BASAN' as 'Balancing Actions for Sustainable Agriculture and Natural Resources'. I am a Design, Monitoring & Evaluation professional. I hold 1) MSc in Regional and Rural Development Planning, Asian Institute of Technology, Thailand, 2002; 2) MSc in Statistics, Tribhuvan University (TU), Kathmandu, Nepal, 1995; and 3) MA in Sociology, TU, 1997. I have more than 10 years of professional experience in socio-economic research, monitoring and documentation on agricultural and natural resource management. I had worked in Lumle Agricultural Research Centre, western Nepal from Nov. 1997 to Dec. 2000; CARE Nepal, mid-western Nepal from Mar. 2003 to June 2006 and WTLCP in far-western Nepal from June 2006 to Jan. 2011, Training Institute for Technical Instruction (TITI) from July to Sep 2011, UN Women Nepal from Sep to Dec 2011 and Mercy Corps Nepal from 24 Jan 2012 to 14 August 2016 and CAMRIS International in Nepal commencing 1 February 2017. I have published articles to my credit.

Thursday, June 13, 2019

Multiplication Rule of Mutually Exclusive and Inclusive Events, Statistical Note 42

Mutually Exclusive Events: Two events are mutually exclusive if they cannot occur at the same time. In tossing of a coin, either of head or tail flips meaning they are mutually exclusive. An occurrence of head excludes an occurrence of tail in the same toss.

Let H be an event of turning head in a toss of a coin.  Likewise, let T be an event of turning tail in a toss of a coin.  The marginal probability of H, P(H) is one by two, 0.5. Similarly, the marginal probability of T, P(T) is one by two, 0.5. The joint probability of head and tail in a single toss, denoted by P(H and T) is impossible, equal to zero.








Figure 1: Marginal probabilities in tossing of a coin

Likewise, in drawing a card from the deck of 52 cards, the occurrence of an ace card excludes cards of other ranks, two to ten, jack, queen and king. Let A be an event of drawing an ace card.  Likewise, let B be an event of drawing any non-ace card.  The marginal probability of A, P(A) is four by 52 or one by 13. Similarly, the marginal probability of any non-ace card, P(B) is 48 by 52 or 12 by 13. The joint probability of ace and any non-ace card in a single draw, denoted by P(A and B) is impossible, equal to zero.









Figure 2: Marginal probabilities in drawing a card from a deck

Mutually Inclusive Events: Two events are mutually inclusive or non-exclusive if the occur of an event does not exclude the occurrence of another event at the same time. In drawing a card from the deck of 52 cards, the occurrence of an ace card does not exclude the occurrence of a club card. Because, both identities - ace as a rank and club as a suit exist on the same card.


Let A be an event of drawing an ace card.  Likewise, let B be an event of drawing any non-ace card.  The marginal probability of A, P(A) is four by 52 or one by 13. Similarly, the marginal probability of any non-ace card, P(NA) is 48 by 52 or 12 by 13. Likewise, let C be an event of drawing a club card and NC be an event of drawing a non-club card. The joint probability of ace and club card in a single draw, denoted by P(A and C) is the product of P(A) and P(C), equal to 0.0192. Similarly, P(A and NC), P(NA and C) and P(NA and NC) are equal to 0.056, 0.2307 and 0.6923 respectively as shown in Figure 3.








Figure 3: Marginal probabilities of mutually exclusive events and joint probability of mutually inclusive events in a draw of a card from the deck

No comments:

Post a Comment