Chapter 2 Exercises
Coin tossing
Solutions

1. Write your own BUGS code for calculating the probability of obtaining at least 15 heads in 20 tosses of a fair coin.

model {
Y ~ dbin(0.5, 20)
P <- step(Y - 14.5)
}

   node   mean   sd   MC error   2.5%   median   97.5%   start   sample
   P   0.021   0.1434   0.00158   0.0   0.0   0.0   1   10000
   Y   10.02   2.244   0.02181   6.0   10.0   14.0   1   10000

[exercises-ch2-coin-tossing-solutions0][exercises-ch2-coin-tossing-solutions1]


2. Adapt your code to calculate the probability that no more than 6 patients in a group of 30 will fail to respond to a drug with a success probability of 0.7.

Modifications to the code are shown in red below. We first change the success probability from 0.5 (fair coin) to 0.7. Requiring no more than 6 failures is the same as requiring at least 24 successes. Alternatively we could calculate the number of failures, numfail , as 30 - Y, and then compute the required probability directly, as shown below ( P.alt ).

model {
Y ~ dbin(
0.7 , 30 )
P <- step(Y - 23.5 )
numfail <- 30 - Y
P.alt <- step(6.5 - numfail)
}

   node   mean   sd   MC error   2.5%   median   97.5%   start   sample
   P   0.1616   0.3681   0.003231   0.0   0.0   1.0   1   10000
   P.alt   0.1616   0.3681   0.003231   0.0   0.0   1.0   1   10000
   Y   21.01   2.517   0.0246   16.0   21.0   26.0   1   10000
   numfail   8.992   2.517   0.0246   4.0   9.0   14.0   1   10000