in a board game, students draw a number, do n...
in a board game, students draw a number, do not replace it, and then draw a second number. draw a line connecting each event to the correct expression and probability the event occurs. not all choices will be used.\nevent\texpression\tprobability\n3. drawing an odd number, then drawing a 6\t$\frac{1}{8}cdot\frac{0}{7}$\t$\frac{1}{7}$\n4. drawing a 2, then drawing another 2\t$\frac{3}{8}cdot\frac{3}{7}$\t$0$\n5. drawing a 9, then drawing another 9\t$\frac{4}{8}cdot\frac{2}{7}$\t$\frac{1}{28}$\n6. drawing a number divisible by 3, then drawing a 1\t$\frac{1}{8}cdot\frac{1}{7}$\t$\frac{9}{56}$\t$\frac{1}{56}$\t$\frac{2}{8}cdot\frac{1}{7}$
Answer
# Explanation:
## Step1: Determine total number of numbers
There are 8 numbers: 2, 1, 6, 2, 9, 6, 6, 1.
## Step2: Analyze event 3
There are 2 odd - numbered (1, 1) out of 8 numbers for the first draw. Probability of drawing an odd number first is $\frac{2}{8}$. After drawing an odd number, there are 7 numbers left. There are 3 sixes, so probability of drawing a 6 second is $\frac{3}{7}$. The combined probability is $\frac{2}{8}\times\frac{3}{7}=\frac{6}{56}=\frac{3}{28}$.
## Step3: Analyze event 4
There are 2 twos out of 8 numbers for the first draw. Probability of drawing a 2 first is $\frac{2}{8}$. After drawing a 2, there is 1 two left out of 7 numbers. Probability of drawing another 2 second is $\frac{1}{7}$. The combined probability is $\frac{2}{8}\times\frac{1}{7}=\frac{2}{56}=\frac{1}{28}$.
## Step4: Analyze event 5
There is 1 nine out of 8 numbers for the first draw. Probability of drawing a 9 first is $\frac{1}{8}$. After drawing a 9, there are 0 nines left out of 7 numbers. Probability of drawing another 9 second is 0. The combined probability is $\frac{1}{8}\times0 = 0$.
## Step5: Analyze event 6
There are 3 numbers divisible by 3 (6, 6, 6) out of 8 numbers for the first draw. Probability of drawing a number divisible by 3 first is $\frac{3}{8}$. After drawing a number divisible by 3, there are 2 ones out of 7 numbers. Probability of drawing a 1 second is $\frac{2}{7}$. The combined probability is $\frac{3}{8}\times\frac{2}{7}=\frac{6}{56}=\frac{3}{28}$.
# Answer:
3. $\frac{3}{28}$
4. $\frac{1}{28}$
5. 0
6. $\frac{3}{28}$