Toss five fair coins and let x equal the number of tails observed. a. Identify the sample points associated with this experiment, and assign a value of x to each sample point. Then list all the possible values of x. b. Calculate p(x) for the values xequals2 and xequals3. c. Construct a probability histogram for p(x). d. What is P(xequals2 or xequals5)?

a) 5H + 0T (1 combinations out of 32) X=0 --> P(X)=0.03125

4H + 1T (5 combinations out of 32) X=1 --> P(X)=0.15625

3H + 2T (10 combinations out of 32) X=2 --> P(X)=0.3125

2H + 3T (10 combinations out of 32) X=3 --> P(X)=0.3125

1H + 4T (5 combinations out of 32) X=4 --> P(X)=0.15625

0H + 5T (1 combinations out of 32) X=5 --> P(X)=0.03125

b) P(x=2)=0.3125

P(x=3)=0.3125

c) Attached

d) P(x=2 or x=5) = 0.34375

Step-by-step explanation:

a) When tossing five coins, we have this sample points (order doesn't matter in this case). There is a total of 2^5=32 possible combinations.

5H + 0T (1 combinations out of 32) X=0

4H + 1T (5 combinations out of 32) X=1

3H + 2T (10 combinations out of 32) X=2

2H + 3T (10 combinations out of 32) X=3

1H + 4T (5 combinations out of 32) X=4

0H + 5T (1 combinations out of 32) X=5

X can take discrete values from 0 to 5.

5H + 0T (1 combinations out of 32) X=0 --> P(X)=0.03125

4H + 1T (5 combinations out of 32) X=1 --> P(X)=0.15625

3H + 2T (10 combinations out of 32) X=2 --> P(X)=0.3125

2H + 3T (10 combinations out of 32) X=3 --> P(X)=0.3125

1H + 4T (5 combinations out of 32) X=4 --> P(X)=0.15625

0H + 5T (1 combinations out of 32) X=5 --> P(X)=0.03125

b) P(x=2)=10/32=0.3125

P(x=3)=10/32=0.3125

c) Attached

d) P(x=2 or x=5) = P(2) + P(5) = 0.3125 + 0.03125 = 0.34375

check the picture below.

well, the angle at the vertex d is clearly not a right-angle, let's check for the one at the vertex f which does look like,   however if it's indeed, that means ef is perpendicular to df, in which case their slopes will be negative reciprocal of each other.

so the negative reciprocal of the slope of ef is 1, however the slope of df is not 1, is 1/2, so nope, they're not perpendicular lines.