Four cards are shuffled and placed face down in front of you. Their faces (hidden) display the four elements: water, earth, wind, and fire. You are to turn the cards over one card at a time until y ou either win or lose. You win if both the water and earth cards are turned over. You lose if the fire card is turn ed over. What is the probability of winning?

Accepted Solution

Answer:probability of winning is[tex]\frac{2}{3}[/tex]Step-by-step explanation:As it is given , 4 cards are available,  there are 4!  mean total possible way of ordering is 24  following are the cases of loosing 1) first card is fire. Thus there are 3! = mean 6 possible ways for particular ordering  to occur. 2) If wind is first card and Fire is second. Then, There are 2! = 2 ways to occur. Hence, the probabiIity of losing is given as  [tex]= \frac{6+2}{24}=\frac{1}{3}[/tex]therefore probality of winning is [tex]1 -\frac{1}{3}[/tex]probality of winning is[tex]\frac{2}{3}[/tex]