Question

# Which of the following probabilities CANNOT be found using the binomial distribution? a) The probability that...

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)

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

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.