Question

Based on the data in this two-way table, which statement is true ?

Answer 1

P(flower is hibiscus | colour is pink) is not equal to P(flower is hibiscus)

Answer 2

Answer:

The correct option is:

        P(flower is hibiscus | color is red)=P(flower is hibiscus)

Step-by-step explanation:

We are given a table as:

Type of Flower/Color      Red         Pink           Yellow     Total

      Rose                           40           20                45          105  

     Hibiscus                      80           40                 90          210

     Total                            120          60                135          315

A)

P(flower is yellow|flower is rose)≠P(flower is yellow)

We know that:

P(A|B) is given by:

  $P(A|B)=\dfrac{P(A)\bigcap B)}{P(B)}$

Here let A= Flower is yellow.

B= flower is rose.

A∩B=flower is a yellow rose.

P(A∩B)=45/315=1/7

P(B)=105/315=1/3

P(A)=135/315=3/7

Hence,

$P(A|B)=\dfrac{\dfrac{1}{7}}{\dfrac{1}{3}}\\\\\\P(A|B)=\dfrac{3}{7}$

Hence, we have:

$P(A|B)=P(A)$

This means that:

P(flower is yellow|flower is rose)=P(flower is yellow)

Hence, option: A is incorrect.

B)

P(flower is hibiscus | color is red)=P(flower is hibiscus)

Let A=flower is hibiscus.

B=color is red.

A∩B=flower is red hibiscus.

Hence,

P(A)=2/3

P(B)=8/21

P(A∩B)=16/63

$P(A|B)=\dfrac{\dfrac{16}{63}}{\dfrac{8}{21}}\\\\\\P(A|B)=\dfrac{2}{3}=P(A)$

Hence, we get:

P(flower is hibiscus | color is red)=P(flower is hibiscus)

              Hence, option: B is correct.

C)

P(flower is rose | color is red)=P( Flower is red)

Let A=flower is rose

B= color is red.

A∩B=flower is red rose

Hence,

P(A)=1/3

P(B)=8/21

P(A∩B)=8/63

Hence, we have:

$P(A|B)=\dfrac{1}{3}\neq P(B)$

Hence, option: C is incorrect.

D)

P(flower is hibiscus | color is pink)≠P(flower is hibiscus)

Let A=flower is hibiscus.

B= color is pink.

A∩B=flower is pink hibiscus.

Hence,

P(A)=2/3

P(B)=4/21

P(A∩B)=8/63

$P(A|B)=\dfrac{\dfrac{8}{63}}{\dfrac{4}{21}}\\\\\\P(A|B)=\dfrac{2}{3}=P(A)$

Hence, we get:

P(flower is hibiscus | color is red)=P(flower is hibiscus)

            Hence, this option is incorrect.