Question

(1 point) Rework problem 27 from section 3.2 of your text, involving the mice in a cage. For this problem, assume there are 6 grey females, 6 grey males, 5 white females, and 3 white males. As in the book, the biologist selects two mice randomly.

(1) What is the probability of selecting two males given that both are grey?

(2) What is the probability of selecting one male and one female given that both are grey?

Answer 1

GIVEN:

The biologist has mice in a cage: grey females, grey males, white females, and white males. He selects two mice randomly.

SOLUTION:

(1) PROBABILITY OF SELECTING TWO MALES GIVEN THAT BOTH ARE GREY:

There are three ways of choosing two grey mice.

• We can choose 2 from grey females (or)
• We can choose 2 from grey males (or)
• We can choose 1 from grey females (and) We can choose 1 from grey males.

Number of ways of choosing two grey mice

  

  

Number of ways of choosing two gray males {We choose two males from 6 grey males}

  

  

  

We know that probability is given by,

Probability = Number of favourable outcomes / Total number of outcomes

The probability of choosing two males given that both are grey = Number of ways of choosing two gray males / Number of ways of choosing two grey mice

  

  

The probability of choosing two males given that both are grey is .

(2) PROBABILITY OF SELECTING ONE MALE AND ONE FEMALE GIVEN THAT BOTH ARE GREY:

There are three ways of choosing two grey mice.

• We can choose 2 from grey females (or)
• We can choose 2 from grey males (or)
• We can choose 1 from grey females (and) We can choose 1 from grey males.

Number of ways of choosing two grey mice

  

  

Number of ways of choosing one grey male and one grey female {We choose 1 male from 6 grey males and 1 female from 6 grey females}

  

  

We know that the probability is given by,

Probability = Number of favourable outcomes / Total number of outcomes

The probability of choosing one male and one female given that both are grey = Number of ways of choosing one grey male and one grey female/ Number of ways of choosing two grey mice

  

  

The probability of choosing one male and one female given that both are grey is .