Chapter PIV, Problem 32RE

(a)

To determine

To find: the probability that the same colour shirt will be available to all four children.

Answer to Problem 32RE

1/54

Explanation of Solution

Given:

There are 4 teams in each age group.

1 of the 4 terms belongs to each boy.

Calculation:

Suppose the 4 colours of teams.

Four colours are available: green (G), blue (B), red (R)and white (W).

Consider GBRW. For one age group, it is green, blue for one of the terms in the second age group, red for one of the third age group teams, and white for one of the fourth age group teams.

The total number of combinations that are possible is $4\times 4\times 4\times 4=256$

WWWW, RRRR; BBBB and GGGG are the favourable combinations that would get the same-colours shirt for four girls.

We have the same chance of a successful 4-color result,

  $\begin{array}{l}=\frac{4}{256}\\ =\frac{1}{54}\end{array}$

(b)

To determine

To find: the probability of all 4 having white shirts.

Answer to Problem 32RE

1/256

Explanation of Solution

WWWW, which happens only once, is a desirable result that all 4 can get white.

Probability, therefore, is $\frac{1}{256}$

(c)

To determine

To find out: how does the probability determined in part (b) alter that.

Answer to Problem 32RE

1/96

Explanation of Solution

The probability would be $\frac{1}{6}\times \frac{1}{4}\times \frac{1}{4}$

Which is $\frac{1}{96}$ .