Question

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.

Answer 1

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).