Question

Whooping cough (pertussis) is a highly contagious bacterial
infection that was a major cuase of childhood deaths before the
development of vaccines. About 80%80% of unvaccinated children who
are exposed to whooping cough will develop the infection, as
opposed to only about 5%5% of vaccinated children.

A group of 18 children at a nursery school are exposed to whooping
cough by playing with an infected child. If all 18 children have
been vaccinated, then what is the probability that no more than 4
of the 18 children develop infections?

Answer #1

It is given that 5% of vaccinated children will develop an infection i.e p = 0.05

This is a binomial distribution as it has just two outcomes - infection or no infection.

n = 18 students

We need to find: P(X <= 4)

From the binomial formula,

P(X <= 4) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4)

X |
p(x) |

0 | 0.397 |

1 | 0.376 |

2 | 0.168 |

3 | 0.047 |

4 | 0.009 |

Total |
0.998 |

Hence, the probability that no more than 4 of the 18 children
will develop infections is **0.998**

Whooping cough (pertussis) is a highly contagious bacterial
infection that was a major cause of childhood deaths before the
development of vaccines.
About 80% of unvaccinated children who are exposed to whooping
cough will develop the infection, as opposed to only about 5% of
vaccinated children.
The following exercise is based on this information.
A group of 20 children at a nursery school are exposed to whooping
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