A coin will be tossed 7 times. Find the probability that there
will be exactly 2 heads among the first 4 tosses, and exactly 2
heads among the last 3 tosses. (Include 2 digits after the decimal
point.)
A fair coin is tossed 100 times. What is the probability of
observing at least 55 heads P(x≥55)? (Approximate the binomial
distribution with a normal distribution
A fair coin is tossed 25 times. What is the probability that at
least 1 tail occurs?
a) 1
b) 0.00000075
c) 0.99999923
d) 0.00000003
e) 0.99999997
f) None of the above.
A business organization needs to make up a 5 member fund-raising
committee. The organization has 9 accounting majors and 7 finance
majors. What is the probability that at most 2 accounting majors
are on the committee?
a) 0.0151
b) 0.0048
c) 0.3654
d) 0.0103
e) 0.3606
f) None...
If a symmetric coin is tossed 100 times, by using normal
approximation find the probability that:
a. it comes up H more than 60 times
b. the number of H(X) is between 60 and 90 (60≤X≤90)
8. A fair coin is tossed 60 times. Find the probability that the
head appears between 22 and 40 times by using
a. binomial distribution,
b. approximation of Binomial distribution by normal
distribution. Discuss why b. is better in practice.
Suppose you toss a fair coin 10 times.
(a) Calculate the probability of getting at least 6 heads, using
the exact distribution.
(b) Now repeat the calculate above, but approximate the
probability using a normal random variable. Do your calculation
both with and without the histogram correction. Which one is closer
to the true answer?
Now suppose you toss a fair coin 1000 times.
(c) What is the probability of getting at least 520 heads? You
can approximate this using...