Question

Out of 18 people in a room, 2 have red hair. What is the probability that a person picked at random from the room does NOT have red hair?

Give an explanation plz:)​

Answer 1

• Total number of people in the room = 18

• Number of people with red hair = 2

• Number of people not with red hair = 18 - 2 = 16

• Probability of picking a person who doesn't have red hair =
  `\sf(Number\:of\:favourable\:outcomes)/(Total\:outcomes)`

Probability = 16/18

Reduce the fraction with 2

Probability = 8/9

Answer 2

`\implies\boxed{\red{\sf P( not \ having\ red\ hair)=( 8)/(9)}}`

Explanation:

Given :-

• There are 18 people in the room .
• Two of them have Red hair.

And we need to find the probability that a person picked at random from the room does not have red hair . So for that firstly let us find how many people do not have red hair.

According to Question :-

`\implies n_((red))+ n_((not\ red))= 18 \\\\\implies 2 + n_((not\ red))= 18 \\\\\implies n_((not\ red))= 18 -2 =\boxed{\red{16}}`

Hence the probability is :-

`\implies P( not \ having\ red\ hair)=( n_((favourable\ outcomes)))/(n_((possible\ outcomes))) \\\\\implies P( not \ having\ red\ hair)=( 16)/(18) \\\\\implies\boxed{P( not \ having\ red\ hair)=( 8)/(9)}`

Hence the required probability is 8/9 .