Question

You pick a card at random. Without putting the first card back, you pick a second card at random.What is the probability of picking a 7 and then picking a number less than 5?

Simplify your answer and write it as a fraction or whole number.

Answer 1

`Probability\ of\ picking\ a\ 7=(1)/(10)\\Probability\ of\ picking\ a\ card\ less\ than\ 5=(4)/(9)`

Explanation:

`We\ are\ given\ that,\\The\ total\ outcomes\ to\ the\ Random\ Experiment\ A\ are\ 1,2,3,4,5,6,7,8,9,10.\\ (We\ don't\ consider\ Ace\ Cards\ or\ Face\ Cards, here.)\\Hence,\\Lets\ consider\ picking\ the\ first\ Card:\\\\Here,\\The\ favorable\ condition\ is\ getting\ a\ 7.\\ No.\ of\ favorable\ elementary\ events=1\\ Total\ no.\ of\ elementary\ events=10\\ We\ know\ that,\\`

`Probability[of\ an\ Event\ A]=(Favourable\ no.\ of\ elementary\ events\ to\ A)/(Total\ no.\ of\ elementary\ events)\\Probability[of\ picking\ a\ 7]=(1)/(10)`

`Now,\\As\ we've\ already\ picked\ a\ card[i.e\ 7],\\The\ total\ outcomes\ to\ the\ Random\ Experiment\ A\ are\ 1,2,3,4,5,6,8,9,10.\\Hence,\\Lets\ consider\ picking\ another\ card\ less\ than\ 5:\\Here,\\The\ favorable\ condition\ is\ picking\ a\ card\ less\ than\ 5.\\Hence,\\The\ favorable\ outcomes\ are\ 1,2,3,4.\\No.\ of\ favorable\ elementary\ events=4\\Total\ no.\ of\ elementary\ events=9\\As\ we\ already\ know\ that,\\`

`Probability[of\ an\ Event\ A]=(Favourable\ no.\ of\ elementary\ events\ to\ A)/(Total\ no.\ of\ elementary\ events)\\Probability[of\ picking\ a\ card\ less\ than\ 5]=(4)/(9)`