When a certain type of thumbtack is flipped, the probability of its landing tip up (u) is 0.54 0.54 and the probability of its landing tip down (d) is 0.46 0.46. suppose you flip two such thumbtacks, one at a time. the probability distribution for the possible outcomes of these flips is shown below. a. find the probability of getting 0 ups, 1 up, or 2 ups when flipping two thumbtacks. b. make a probability distribution graph of this.

Part A. In probability and statistics, there is an equation for repeated trials. This is useful for situations like tossing a coin or rolling a dice. Each possible result of a situation has its own probability of p. You want to find the total probability of getting 'r' number of successes out of 'n' trials. The equation is

P = n!/r!(n-r!) * p^(n-r) * q^r, where
n is the number of trials; in this case n=2
r is the number of times an event can happen successfully
p is the probability of that success
q is the probability of failing; note that p+q=1

The p for ups is 0.54, while q is 0.46. When r=0 ups
P = 2!/0!(2-0!) * (0.54)^(2-0) * (0.46)^0
P = 0.2916

The same thing is done to r=1 and r=2. The complete table is shown below

     r            P
    0         0.2916
    1         0.4968
    2         0.2116

When you graph r against P, you will get a probability distribution graph as shown in the picture (Part B).