Question

Suppose you are playing a game with two number cubes. Let A represent rolling 2, 3, or 4, and B represent rolling 1, 5, or 6. The probability of A is 1/2 and the probability of B is 1/2 .

a. Simplify (1/2 a + 1/2 b) ^2

b. What is the probability that one number cube shows 2, 3, or 4, and the other shows 1, 5, or 6?

Answer 1

1. Use:
\[(a + b)^2 = a^2 + b^2 + 2ab\]

\[= \frac{a^2}{4} + \frac{b^2}{4} + \frac{a \times b}{2}\]

As a = 1/2 and b = 1/2

\[= \frac{1}{16} + \frac{1}{16} + \frac{1}{8} = \frac{1 + 1 + 2}{16} = \frac{4}{16} = \frac{1}{4}\]

Answer 2

b>

\[P = \frac{1}{3} \times \frac{1}{3} = \frac{1}{9}\]

Answer 3

thanks!

Answer 4

Welcome dear..