Which of these problems could be figured out using the binomial distribution? Ci

Question

Which of these problems could be figured out using the binomial distribution? Circle the letter for any that work. 2. (a) Figuring out the probability of exactly 8 heads in 20 coin tosses. (b) Figuring out the probability of being dealt a royal flush in poker. (c) Finding the probability of 4 or more sixes when rolling a fair die 15 times in a row. (d) Finding the probability that the fourth roll of a die yields the first 6. Give a brief explanation for why the binomial distribution would not apply to each uncircled one:

Explanation / Answer

The binomial distribution is applicable for only a) problem, i.e. Figuring out the probability of exactly 8 heads in 20 coins tosses.

For the other problems binomial distribution is not suitable, because these problems are not satisfying the physical conditions for the Binomial distribution,

In all problems are outcomes are more than two, i.e 4 or more sixes means the outcomes may be 4 or 5 or 6 sixes. (but not only two exhaustive and mutually disjoint outcomes), hence binomial distribution is not suitable.

The probability of success p is not constant for each trial, i.e. like in royal flush in Poker.

Hence binomial distribution is not suitable for (b), (c) and (d) problems

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