Chapter 11.4, Problem 71S

To determine

To find the probability if she randomly selects $4$ CDs.

Answer to Problem 71S

  $\boxed{0.36}$

  $\boxed{0.42}$

  $\boxed{0.05}$

Explanation of Solution

Given information:

Tina owns $11$ pop, $6$ country, $16$ rock, and $7$ rap CDs. Find each probability if she randomly selects $4$ CDs.

  $a.$ $p\left(2rock\right)$

  $b.$ $p\left(1rap\right)$

  $c.$ $p\left(1rock\&2country\right)$

Calculation:

Here, we will consider that a girl $T$ owns $11P$ type, $6C$ type, $16O$ type, and $7A$ type CDs. So, the number of CDs in her collection is, $11+6+16+7=50$

She selects $4$ CDs from her collection at random.

Generally, the probability of event $E$ is,

  $P\left(E\right)=\frac{Numberoffavourableoutcomes }{totalnumberofoutcomes}$

  $\left(a.\right)$ Now, we will consider the probability that the girl $T$ selects $2O$ type CDs.

As she selects $2$ of $6O$ type CDs and the $2$ from the remaining $50-16=34$ CDs, the probability is,

  $P\left(2O\right)=\frac{C{}_2\times C{}_2}{C{}_4}=0.36$

Hence, the probability that the girl $T$ selects $2O$ type CDs is $\boxed{0.36}$ .

  $\left(b.\right)$ Now, we will consider the probability that the girl $T$ selects $1A$ type CD.

As she selects $1$ of $7O$ type CDs and the $3$ from the remaining $50-7=43$ CDs, the probability is,

  $P\left(1A\right)=\frac{C{}_1\times C{}_3}{C{}_4}=0.42$

Hence, the probability that the girl $T$ selects $1A$ type CD is $\boxed{0.42}$ .

  $\left(c.\right)$ Now, we will consider the probability that the girl $T$ selects $1O$ and $2C$ type CDs.

As she selects $1$ of $7O$ type CDs, $2$ of $6C$ type CDs and the $1$ from remaining $50-7-6=37$ CDs, the probability is,

  $P\left(1A\right)=\frac{C{}_1\times C{}_2\times C{}_1}{C{}_4}=0.05$

Hence, the probability that the girl $T$ selects $1O$ and $2C$ type CDs is $\boxed{0.05}$ .