Question

13. The following table identifies a group of children by one of four hair colors, and by type of hair.

Hair Type	Brown	Blond	Black	Red	Totals
Wavy	21		16	5	48
Straight	78	13		14
Totals		19			218

• 
  part (b)

• What is the probability that a randomly selected child will have wavy hair? (Enter your answer as a fraction.)

• Part (c)
  What is the probability that a randomly selected child will have either brown or blond hair? (Enter your answer as a fraction.)

• Part (d)
  What is the probability that a randomly selected child will have wavy brown hair? (Enter your answer as a fraction.)

• Part (e)
  What is the probability that a randomly selected child will have red hair, given that he has straight hair? (Enter your answer as a fraction.)

• Part (f)
  If B is the event of a child having brown hair, find the probability of the complement of B. (Enter your answer as a fraction.)

• Part (g)
  If B is the event of a child having brown hair, what does the complement of B represent?

• The complement of B would be the event of a child having blond or black hair.

• The complement of B would be the event of a child having wavy or straight hair.    

• The complement of B would be the event of a child not having brown hair.

• The complement of B would be the event of a child having blond hair.

Answer 1

Some data are missing in the question, Below is the completed table:

Hair Type	Brown	Blond	Black	Red	Totals
Wavy	21	6	16	5	48
Straight	78	13	65	14	170
Totals	99	19	81	19	218

(b) Total no. of children = 218

No. of children with wavy hair = 48

The probability that a randomly selected child will have wavy hair = 48/218

(c) Children having brown hair = 99; Children having blonde hair = 19

No. of children having brown or blonde hair = 99+19 = 118

The probability that a randomly selected child will have either brown or blond hair = 118/218

(d) No. of children having wavy brown hair = 21

The probability that a randomly selected child will have wavy brown hair = 21/218

(e) No. of children having sraight hair = 170

Among the children having straight hair, no. of children having red hair = 14

The probability that a randomly selected child will have red hair, given that he has straight hair = 14/170

(f) B: a child has brown hair

P(B) = 99/218

Complement event of B is denoted as Bc

P(Bc) = 1 - 99/218 = 119/218

(g) If B is the event of a child having brown hair, the complement of B represents:

• The complement of B would be the event of a child not having brown hair.

Please rate if satisfied.