CS206 -Discrete Mathematics II Instructor: Chitoor V.Srinivasan PROBLEM SET 8 SOLUTIONS
It's Binomial distribution. We have .
(a).
We have here.
(b).
We have here.
It's a Bernoulli Trial. We have .
(a).
Binomial distribution
(b).
Since each toss is independent, it's a Geometric distribution.
(c).
Binomial Distribution
It's also Binomial distribution. We have .
(a).
(b).
(c).
Binomial Distribution. Assume that 143 is the expected number
of errors over the total of characters. Then
the probability of any one character being in error is .
Then
(a).
the probability that a page has no errors is
.
(b).
the probability that a page has no more than 2 errors is
When we draw balls out of the bag, with replacement, it's a
Binomial distribution, we have
When we draw balls out of the bag, without replacement. It's
Hypergeometric distribution (according to Theorem 3.6.3),
we have
We draw cards from the pack without replacement. Again,
Hypergeometric distribution:
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
This uses Poisson distribution. John makes an average of
2.4
telephone calls in an hour, in other word .
This is also Poisson distribution. The claim that one out every
fifty books brought out is a bestseller means . When it is
known that at least two of its books are best
sellers, this problem really is a condition probability problem.
Also Poisson distribution. As we know that we can use
Binomial distribution to approximate it, we have .