215k views
0 votes
Thirty students in the fifth grade class listed their hair and eye colors in the table below:Are the events "brown hair" and "brown eyes" independent? A.) Yes, P(brown hair) ⋅ P(brown eyes) = P(brown hair ∩ brown eyes)B.) Yes, P(brown hair) ⋅ P(brown eyes) ≠ P(brown hair ∩ brown eyes)C.) No, P(brown hair) ⋅ P(brown eyes) = P(brown hair ∩ brown eyes)D.) No, P(brown hair) ⋅ P(brown eyes) ≠ P(brown hair ∩ brown eyes)

Thirty students in the fifth grade class listed their hair and eye colors in the table-example-1
User Foundry
by
8.0k points

1 Answer

3 votes

Let us begin by defining an independent event

Two events A and B are said to be independent if the fact that one event has occurred does not affect the probability that the other event will occur.

For independent events A and B:


P(A\text{ and B\rparen = P\lparen A\rparen }*\text{ P\lparen B\rparen}

The two events under study are

- Brown hair

- Brown eyes

The probability of a brown hair:


P(brown\text{ hair\rparen = }(19)/(30)

The probability of brown eyes:


P(brown\text{ eyes\rparen = }(15)/(30)

The probability of brown hair and brown eyes:


P(brown\text{ hair and brown eyes\rparen = }(10)/(30)

Check:

The events would be independent if:


P(brown\text{ hair and brown eyes\rparen = P\lparen brown hair\rparen }*\text{ P\lparen brown eyes\rparen}
\frac{10}{30\text{ }}\text{ }\\e(19)/(30)\text{ }*(15)/(30)

Hence, the correct option is No, P(brown hair) . P(brown eyes) ≠ P(brown hair ∩ brown eyes)

Answer: Option D

User Arkku
by
8.7k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories