From each of 100 concrete mixes six sample blocks were taken and subjected to strength tests, the number out of the six blocks failing the test being recorded in the following table:

$$\begin{array}{lrrrrrrr} \text { No. } x \text { failing strength tests } & 0 & 1 & 2 & 3 & 4 & 5 & 6 \\ \text { No. of mixes with } x \text { failures } & 53 & 32 & 12 & 2 & 1 & 0 & 0 \end{array}$$

On the assumption that the probability of failure is the same for each block, obtain an unbiased estimate of this probability and explain how to find a $95 \%$ confidence interval for it.