Interactive practice questions
A dog has three puppies.
Let $M$M represent the number of male puppies in this litter.
If a dog has $3$3 puppies, then the number of male puppies, $M$M, can be $0$0, $1$1, $2$2 or $3$3.
What are the values of the proportions, $\hat{P}$^P of male puppies in the litter associated with each outcome of $M$M?
If $M=0$M=0: $\hat{P}$^P$=$=$\editable{}$
If $M=1$M=1: $\hat{P}$^P$=$=$\editable{}$
If $M=2$M=2: $\hat{P}$^P$=$=$\editable{}$
If $M=3$M=3: $\hat{P}$^P$=$=$\editable{}$
Construct the probability distribution for $M$M and $\hat{P}$^P below.
| $m$m | $0$0 | $1$1 | $2$2 | $3$3 |
|---|---|---|---|---|
| $P$P$($($M=m$M=m$)$) | $\frac{1}{8}$18 | $\editable{}$ | $\editable{}$ | $\editable{}$ |
| $\hat{p}$^p | $0$0 | $\frac{1}{3}$13 | $\frac{2}{3}$23 | $1$1 |
| $P$P$($($\hat{P}=\hat{p}$^P=^p$)$) | $\editable{}$ | $\frac{3}{8}$38 | $\editable{}$ | $\editable{}$ |
Use your answers from part (b) to determine $P$P$($($\hat{P}>\frac{1}{2}$^P>12$)$).
Three marbles are randomly drawn from a bag containing five black and six grey marbles.
Let $X$X be the number of black marbles drawn, with replacement.
A company wants to know the likelihood of securing sales with potential clients.
Historically, the company has $70$70 successful sales for every $100$100 potential clients contacted.
Let $X$X be the number of sales the company secures within the next $4$4 potential clients.
A pencil case contains $9$9 red pens and $7$7 black pens. $4$4 pens are drawn randomly from the pencil case, one at a time, each being replaced before the next one is drawn.
Let $W$W be the number of red pens drawn.