Question

puzzle #5
find the probability
answer choices
a: $\frac{3}{8}$ b: $\frac{4}{7}$ c: 0
d: $\frac{3}{7}$ e: $\frac{5}{8}$ f: $\frac{15}{64}$
g: $\frac{1}{2}$ h: $\frac{25}{64}$ i: 1

1. that the bean - bag you throw will land on an odd number.
2. that the bean - bag you throw will land on an even number.
3. that after 2 throws, the bean - bag will first hit an even, then hit an odd.
4. that after 2 throws, the bean - bag will hit 2 odds in a row.

type the 4 - letter code next to the answer box. all caps, no spaces.

Explanation:

Step1: Count total and odd - numbered regions

There are 8 numbered regions in total. The odd - numbered regions are 1, 3, 5, 7, so there are 4 odd - numbered regions.
The probability of landing on an odd number $P(O)=\frac{\text{Number of odd - numbered regions}}{\text{Total number of regions}}=\frac{4}{8}=\frac{1}{2}$. So the answer for 1 is G.

Step2: Count total and even - numbered regions

The even - numbered regions are 2, 4, 6, so there are 3 even - numbered regions.
The probability of landing on an even number $P(E)=\frac{\text{Number of even - numbered regions}}{\text{Total number of regions}}=\frac{3}{8}$. So the answer for 2 is A.

Step3: Calculate probability of even then odd

The probability of hitting an even number on the first throw is $\frac{3}{8}$, and the probability of hitting an odd number on the second throw is $\frac{4}{8}$.
Since the throws are independent events, the probability of first hitting an even then an odd is $P = \frac{3}{8}\times\frac{4}{8}=\frac{12}{64}=\frac{3}{16}$ (not in the options, there may be a mistake in the problem - setup or options).

Step4: Calculate probability of two odds in a row

The probability of hitting an odd number on the first throw is $\frac{4}{8}$, and the probability of hitting an odd number on the second throw is also $\frac{4}{8}$.
Since the throws are independent events, the probability of hitting two odds in a row is $P=\frac{4}{8}\times\frac{4}{8}=\frac{16}{64}=\frac{1}{4}$ (not in the options, there may be a mistake in the problem - setup or options).

Answer:

1. G
2. A
3. (No correct option)
4. (No correct option)