7.10 The Binomial Distribution

Decide whether each of the following is a binomial experiment. For those that aren’t, identify which criterion or criteria are violated.

1. You roll a standard 6-sided die 10 times and write down the number that appears each time.
2. You roll a standard 6-sided die 10 times and write down whether the die shows a 6 or not.
3. You roll a standard 6-sided die until you get a 6.
4. You roll a standard 6-sided di…

1. Find the probability of rolling a standard 6-sided die 4 times and getting exactly one 6 without using technology.
2. Find the probability of rolling a standard 6-sided die 60 times and getting exactly ten 6s using technology.
3. Find the probability of rolling a standard 6-sided die 60 times and getting exactly eight 6s using technology.

Suppose we are about to flip a fair coin 50 times. Let $H$ represent the number of heads that result from those flips. Use technology to find the following:

1. $P \left(H \leq 22\right)$
2. $P \left(H < 26\right)$
3. $P \left(H > 28\right)$
4. $P \left(H \geq 20\right)$
5. $P \left(20 < H < 25\right)$