Question

The following Venn diagram is an example of the outcomes of flipping three coins. HHTTHT HTH TTH HTT Please use a Venn diagram to describe the outcomes of flipping FOUR coins and mark the outcomes. A particular iPod playlist contains 100 songs, 10 of which are by the Beatles. Suppose the shuffle feature is used to play the songs in random order with no repeating. What is the probability that the first Beatles song heard is the fifth song played? What is the probability that there are exactly two Beatles songs in the first five songs played?

Answer 1

total songs ,n = 100

probability of Beatles songs,p  = 10/100 = 0.1

a) P(first Beatles songs is fifth song) =P(first four are non Beatle and fith is Beatle song)=( (1-p)^4*p = 0.9^4*0.1=0.06561

b)

it is a binomial probability distribution,          
          
and probability is given by          
          
P(X=x) = C(n,x)*p^x*(1-p)^(n-x)  

       
P ( X =    2   ) = C(   5   ,   2   )*   0.10   ^   2   *   0.90   ^   3

=0.0729