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 beanbag you throw will land on an odd number.
2 that the beanbag you throw will land on an even number.
3 that after 2 throws, the beanbag will first hit an even, then hit an odd.
4 that after 2 throws, the beanbag will hit 2 odds in a row.
type the 4 - letter code into the answer box. all caps, no spaces.
your answer

Explanation:

Step1: Count total and odd - numbered squares

There are 8 squares in total. The odd - numbered squares are 1, 3, 5, 7, so there are 4 odd - numbered squares.
The probability of landing on an odd number in one throw, $P(O_1)=\frac{4}{8}=\frac{1}{2}$.

Step2: Count even - numbered squares

The even - numbered squares are 2, 4, 6, so there are 3 even - numbered squares.
The probability of landing on an even number in one throw, $P(E_1)=\frac{3}{8}$.

Step3: Probability of even then odd in two throws

Since the throws are independent events, the probability of hitting an even number first and then an odd number is $P(E_1)\times P(O_2)$. Since the probabilities remain the same for each throw, $P = \frac{3}{8}\times\frac{4}{8}=\frac{12}{64}=\frac{3}{16}$.

Step4: Probability of two odds in a row

Since the throws are independent events, the probability of hitting an odd number twice in a row is $P(O_1)\times P(O_2)=\frac{4}{8}\times\frac{4}{8}=\frac{16}{64}=\frac{1}{4}$.

1. For the probability of landing on an odd number:

• The answer is $\frac{1}{2}$, which corresponds to option G.

1. For the probability of landing on an even number:

• The answer is $\frac{3}{8}$, which corresponds to option A.

1. For the probability of hitting an even then an odd in two throws:

• $\frac{3}{16}=\frac{12}{64}$, and there is no exact match among the given options.

1. For the probability of hitting two odds in a row:

• The answer is $\frac{1}{4}=\frac{16}{64}$, and there is no exact match among the given options.

Answer:

1. G
2. A
3. No match
4. No match