Statistics: Binomial Probability - Coin Toss Problem

Question :
If a fair coin is tossed 200 times, what is the probability that the coin lands tails less than 75 times?

Solution Summary

The solution to the posted question is given using step by step method with explanation in the attached document.
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A cointossed 10,000 times. Heads appears 5100 times. Do you think the
coin is fair at the 0.05% level of significance? at the 0.01% level of
significance?

Consider a state lottery that has a weekly television show. On this show, a contestant receives the opportunity to win $1 million. The contestant picks from 4 hidden windows. Behind each is one of the following: $150,000, $200,000 $1 million, or a "stopper". Before beginning, the contestant is offered $100,000 to stop. Mathemati

A) A coin is tossed 20 times. Find probability of getting at least 14 heads.
B) A die is tossed 20 times. Find probability of getting a "1" two times.
C) Three dice are tossed. Find probability that a four shows on exactly two of the dice.

Please help show me how to do a tree diagram for this problem and proving step-by-step solution to make sure the rest of the problem is correct.
14. Suppose you perform a probability experiment in which you toss a fair coin and then roll a fair number cube with the faces labeled with numbers 1 through six.
a. Draw a tree

Suppose a fair coin is tossed n times. The probability of obtaining head and tail are the same because this is a fair coin. The proportion of heads is defined as the number of heads appeared divided by n. We can model this probability distribution by binominal distribution.
For large n, the binominal distribution can be repla

6. A coin is tossed 4 times. Let X denote the number of heads which appear in 4 tosses.
a) Construct a probability distribution for X
b) Find P(X>2)
c) Find the expected value of X
d) Find the variance and standard deviation of X
7. The probability that a randomly selected elementary or secondary school teacher from a cit

When assigning probabilities of two simple events, can we assume that each event is always equally likely to occur and, thus assign .5 to each event? Could you provide an example in your explanation?

Mary Tosses a coin 3 times and john does the same.
A) Find probability Mary obtains one head. I have that answer which i think is 1/33 or 33%, but do I include John's tosses also in that?
b) Find the probability that Mary obtains exactly one head and so does John. Here I thought to do 1/2 times 1/2 = 1/4 is that right?

Problem 1:
In Module 2, you learned how to compute a z-score from a raw score. In this module, you are shown how to estimate the probability of getting a certain z-score value equal to or higher than the one that is observed (i.e., more extreme in the tail), as well as the proportion of all z-values that would NOT be in the ta