Perform the two-coin toss experiment discussed in Appendix 2A by flipping two coins (a penny and a nickel) 50 times and recording the outcome (H or T for each coin) for each flip.

Compute the following:

1. Estimate the probability of two heads given at least one head by counting the number of (H, H) outcomes and dividing by the number of outcomes that have at least one head. How does this compare to the true value of one-third computed in Appendix 2A? (1.25 points)

Suppose we have the following outcomes:

( H , H ) ( T , H ) ( H , T ) ( H , H ) ( T , T )

( H , H ) ( T , T ) ( T , T ) ( H , T ) ( H , T )

( T , H ) ( T , H ) ( T , T ) ( H , H ) ( T , H )

( H , H ) ( H , T ) ( H , T ) ( T , T ) ( H , H )

( H , T ) ( H , T ) ( H , H ) ( H , H ) ( T , H )

( H , T ) ( T , T ) ( H , H ) ( T , T ) ( H , H )

( H , H ) ( T , H ) ( H , H ) ( T , H ) ( T , T )

( T , H ) ( H , H ) ( T , H ) ( H , T ) ( H , H )

( H , H ) ( H , T ) ( H , H ) ( T , T ) ( T , T )

( T , H ) ( H , T ) ( T , T ) ( H , T ) ( H , T )

1. Estimate the probability of two heads given that the penny is a head by counting the number of (H, H) outcomes and dividing by the number of outcomes for which the penny is a head. How does this compare to the true value of one-half computed in Appendix 2A?

(1.25 points)