A biased coin is tossed four times and the number of heads noted. The experiment is performed 500 times in all and the results are summarised in the table: Number of heads Frequency 012 34 12 50 151 200 87

(a) From the experimental data, estimate the probability of obtaining a head when the coin is tossed.

(b) Using a binomial distribution with the same mean, calculate the theoretical probabilities of obtaining 0, 1, 2, 3 and 4 heads.