a middle row on a plane seats 7 people. three of them order chicken (c) and the remaining four pasta (p). the flight attendant returns with the meals, but has forgotten who ordered what and discovers that they are all asleep, so she puts the meals in front of them at random. what is the probability that they all receive correct meals?

Question

16-12-2022
Mathematics

Answered

a middle row on a plane seats 7 people. three of them order chicken (c) and the remaining four pasta (p). the flight attendant returns with the meals, but has forgotten who ordered what and discovers that they are all asleep, so she puts the meals in front of them at random. what is the probability that they all receive correct meals?

Answer :

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qwpen qwpen · Answer 1 · 2022-12-21T11:20:20-05:00

The probability that they all receive correct meals - [tex]\frac{1}{35}[/tex]

To solve the problem we shall have to use the formula of Probability. By the term probability, we mean possibility. It is the branch of mathematics that concerns numerical descriptions of how likely an event is to occur.

We cannot predict the occurrence of a number of events. Then comes the question of probability which means the chances of occurrence or happening. Probability can be ranged from 0 to 1, where 0 means the total impossibility of the event and 1 indicates full certainty of the event.

If we add all the probabilities in a particular event the result comes to 1. The probability formula can be defined as the possibility of an event happening which is equal to the ratio of the number of favorable outcomes and the total number of outcomes.

The probability is :

= [tex]\frac{1}{\frac{7!}{4! * 3!} }[/tex] = [tex]\frac{4! * 3!}{ 7!}[/tex] = [tex]\frac{4 * 3 * 2 * 1 * 3 * 2 * 1}{7 * 6 * 5 * 4 * 3 * 2 *1}[/tex] = [tex]\frac{3 * 2}{5 * 6 * 7}[/tex] = [tex]\frac{1}{35}[/tex]

So,

The probability that they all receive the correct meals = [tex]\frac{1}{35}[/tex] .