CS206 -Discrete Mathematics II
Instructor: Chitoor V.Srinivasan
PROBLEM SET 8 SOLUTIONS

  1. It's Binomial distribution. We have   tex2html_wrap_inline199 .
    (a).
    We have   tex2html_wrap_inline201   here.

    displaymath177

    (b).
    We have   tex2html_wrap_inline203   here.

    displaymath178

  2. It's a Bernoulli Trial. We have   tex2html_wrap_inline205 .
    (a).
    Binomial distribution

    displaymath179

    (b).
    Since each toss is independent, it's a Geometric distribution.

    displaymath180

    (c).
    Binomial Distribution

    displaymath181

  3. It's also Binomial distribution. We have   tex2html_wrap_inline207 .
    (a).

    displaymath182

    (b).

    eqnarray23

    (c).

    eqnarray32

  4. Binomial Distribution. Assume that 143 is the expected number of errors over the total of   tex2html_wrap_inline209   characters. Then the probability of any one character being in error is   tex2html_wrap_inline211 . Then
    (a).
    the probability that a page has no errors is   tex2html_wrap_inline213 .
    (b).
    the probability that a page has no more than 2 errors is

    displaymath183

  5. When we draw balls out of the bag, with replacement, it's a Binomial distribution, we have

    displaymath184

    When we draw balls out of the bag, without replacement. It's Hypergeometric distribution (according to Theorem 3.6.3), we have

    displaymath185

  6. We draw cards from the pack without replacement. Again, Hypergeometric distribution:

    displaymath186

  7. Hypergeometric distribution. If we get more salmons than trouts, then the number of salmons is either  9  or  10. Hence the chance we get more salmons is the sum of the chance we get  9  salmons and we get  10  salmons, which is

    displaymath187

  8. This uses Poisson distribution. John makes an average of  2.4  telephone calls in an hour, in other word   tex2html_wrap_inline225 .

    eqnarray68

  9. This is also Poisson distribution. The claim that one out every fifty books brought out is a bestseller means   tex2html_wrap_inline227 . When it is known that at least two of its books are best sellers, this problem really is a condition probability problem.

    eqnarray100

  10. Also Poisson distribution. As we know that we can use Binomial distribution to approximate it, we have   tex2html_wrap_inline229 .

    eqnarray117

    As we want to get the exact value, we know   tex2html_wrap_inline231 .

    eqnarray129