Question

Which of the following probabilities CANNOT be found using the binomial distribution? a) The probability that 3 out of 8 tosses of a coin will result in heads b) The probability of getting exactly five face cards when drawing five cards without replacement from a standard deck of 52 cards c) When randomly choosing a family with four children, the probability that it will have exactly two boys and two girls as children d) The probability that a student randomly guessing will get at least 8 out of 10 multiple-choice questions correct (assuming every question has five choices)

Answer #1

**Solution:**

We have to find which of the following probabilities CANNOT be found using the binomial distribution.

**Part a)** The probability that 3 out of 8 tosses
of a coin will result in heads

Since n = 8 independent trials , x = number of heads and p = probability of success is constant , thus we can find this probability by using Binomial distribution

**Part b)** The probability of getting exactly five
face cards when drawing five cards without replacement from a
standard deck of 52 cards

Since we are drawing 5 cards without replacement , trials are not independent as well as outcomes are more than 2

**thus this probability can not found by using Binomial
distribution**

**Part c)** When randomly choosing a family with
four children, the probability that it will have exactly two boys
and two girls as children

n = 4 children are independent

Let x = number of boys and p = probability of boy is constant

We have two possible outcomes Boy / Girl

Thus we can find this probability by using Binomial distribution.

**Part d)** The probability that a student randomly
guessing will get at least 8 out of 10 multiple-choice questions
correct (assuming every question has five choices)

n= 10 independent questions

p = probability of correct answer when guessing = 1/5 is constant

x = number of correct answers

we have five multiple choices , but we can split them in two parts : Success = Correct and failure = Incorrect

Thus we can find this probability by using Binomial distribution.

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