what are my odds?

Question

there are 4 cards, one is a hidden joker, i need to find it. i have 2 picks, first pick 1 in 4 chances. if not succesful then i pick again this time 1 in 3 chances. how do i work out my overall chance of picking correctly as it is based over 2 seperate picks at differring odds of success?

Answer 1

Without Replacement

 

P{joker picked on two tries without replacement}

= P{joker picked on 1st try} + P{joker picked on 2nd try}

= ¼ + P{joker picked on 2nd try|joker missed on 1st try}P{joker missed on 1st try}

= ¼ + ¹⁄3 (¾)

= ½

 

With replacement, however, you overall chance will be slightly less

P{joker picked on two tries with replacement}

 

= ¼ + ¼ (¾)

= ⁷/₁₆

 

Per Mark M. comment, you can calculate your odds as P/(1-P) using the above answers.