It might pay to review the Binomial distribution.1. 75% of a community voted Jay Cool as their favourite singer. A random sample of 25 people was taken from this large population. Estimate the chance that

a. everybody in the sample voted him as their favourite singer.

b. exactly 10 individuals in the sample voted him as their favourite singer.

Mr F says: Use the Binomial distribution. n = 25, p = 0.75.

2. 12 students from a school are shortlisted as players for a basketball team. If 15% of the school population were found to be left handed, calculate the probability of

a. all the players being right handed.

b. exactly half of the team is left handed

Mr F says: Use the Binomial distribution. n = 12, p = 0.15. Calculate Pr(X = 0) and Pr(X = 6).

3. Suppose 70% of a herd of cattle is infected with a particular disease. LetYbe the number of diseased cattle in a sample of size 10. What is the probability ofY

b. being more than 8?

- being less than 2?

c. being between 2 to 8 (inclusive)?

Mr F says: Use the Binomial distribution. n = 10, p = 0.7.

4. Consider a family consisting of 8 children. Assuming that the chance of male and female births is the same. What is the probability of the children

Mr F says: Use the Binomial distribution. n = 8, p = 0.5. Calculate Pr(X > 0) = 1 - Pr(X = 0). For the second, I don't get it ..... Do you mean BG and the other 6 don't matter?

- consisting of at least 1 boy?
- consisting of at least 1 girl and 1 boy?

5. Considering the tossing of a pair of fair dice together, what is the probability of

- obtaining a total of 7 in a single toss? Mr F says: Draw a grid and count the favourable outcomes.
- obtaining a total of 7 exactly twice in 6 tosses? Mr F says: Use the Binomial distribution. n = 6, p = probability calculated above.