Question

1. Consider rolling two dice once. Calculate the probability of the...
A, rolling a sum of 5 or an even sum
B, rolling a sum of 7 or 6
C,rolling a sum of 10 or an odd sum

2.six(6) women, 4 men, 3 boys and 7 girls enter a competition. They each have an equally likely chance of winning. What is the probability that the winner will be..
A, female?
B, a child?
C, a man?

Answer 1

1. Rolling two dice once and summing the outcomes is summarized in the following table.

(a). $P(5\cup even)$

The two events (sum of 5 and even sum) are disjoint. Thus,

$P(5\cup even)=P(5)+P(even)$

$P(5)=\frac{4}{36}=\frac{1}{9}$

$P(even)=\frac{18}{36}=\frac{1}{2}$

$P(5\cup even)=\frac{1}{9}+\frac{1}{2}$

$=\frac{11}{18}$

(b). $P(7\cup 6)$

$P(7\cup 6)=P(7)+P(6)$

$=\frac{5}{36}+\frac{6}{36}$

$=\frac{11}{36}$

(c). $P(10\cup odd)$ (disjoint)

$P(10\cup odd)=P(10)+P(odd)$

$=\frac{3}{36}+\frac{18}{36}$

$=\frac{7}{12}$

2.

a. P(female)

6 women and 7 girls out of 20

$P(female)=\frac{13}{20}$

b. P(Child)

3 boys and 7 girls out of 20

$P(Child)=\frac{10}{20}$

$=\frac{1}{2}$

c. P(man)

4 men out of 20

$P(Man)=\frac{4}{20}$

$=\frac{1}{5}$