My Math Forum Probability problem

 February 12th, 2014, 01:44 PM #1 Newbie   Joined: Feb 2014 Posts: 6 Thanks: 0 Probability problem In a woman single badminton match, the first player who wins two out of three sets win the match. The probability of a particular player winning a set is 0.7 if she has won the previous set. The probability of the player winning a set is 0.4 if she lost the previous set. (a) Find the probability that the player wins the match given that she lost the first set. 0.7*0.4 = 0.28 (b) If the probability that the player wins the match is 0.64, find the probability that she wins the first set. No clue, mind giving a tips? I've tried probability tree... and thinking of the rule of total probability.
February 13th, 2014, 04:27 PM   #2
Math Team

Joined: Dec 2006
From: Lexington, MA

Posts: 3,267
Thanks: 408

Re: Probability problem

Hello, ystiang!

Quote:
 In a woman single badminton match, the first player who wins two out of three sets wins the match. The probability of a particular player winning a set is 0.7 if she has won the previous set. The probability of the player winning a set is 0.4 if she lost the previous set. (a) Find the probability that the player wins the match given that she lost the first set. [color=beige]. . [/color]$(0.4)(0.7) \,=\, 0.28$ (b) If the probability that the player wins the match is 0.64, find the probability that she wins the first set.

$\text{\begin{array}{cccccccc}\text{W\!e have:} & P(W|W) \:=\:0.7 && P(L|W) \:=\:0.3 \\ \\ \\
& P(W|L) \:=\:0.4 && P(L|L) \:=\:0.6 \end{array}$

$\text{Let }p\text{= probability that she wins the first set.}$

$\text{There are three scenarios in which she wins the match:}$

$\text{(1) WW: }\:(p)(0.7) \,=\,0.7p$

$\text{(2) WLW: }\:(p)(0.3)(0.4) \,=\,0.12p$

$\text{(3) LWW: }\:(1-p)(0.4)(0.7) \,=\,0.28\,-\,0.28p$

$P(\text{win match}) \:=\:0.7p\,+\,0.12p\,+\,0.28\,-\,0.28p \;=\;0.64$

$\;\;\;0.54p \:=\:0.36 \;\;\;\Rightarrow\;\;\;p \:=\:\frac{0.36}{0.54} \;\;\;\Rightarrow\;\;\; p \:=\:\frac{2}{3}$

 Tags probability, problem

,

,

,

,

# content

Click on a term to search for related topics.
 Thread Tools Display Modes Linear Mode

 Similar Threads Thread Thread Starter Forum Replies Last Post bsjmath Advanced Statistics 2 March 1st, 2014 02:50 PM Vasia Probability and Statistics 0 December 15th, 2012 01:48 AM halloweengrl23 Advanced Statistics 3 March 23rd, 2012 02:27 AM adiptadatta Probability and Statistics 1 May 11th, 2010 06:46 AM indian Algebra 0 February 21st, 2008 04:10 PM

 Contact - Home - Forums - Cryptocurrency Forum - Top