A survey asked students whether they have any siblings and pets. the survey data are shown in the relative frequency table.

Mathematics

1 answer:

PIT_PIT [12.4K]2 months ago

5 0

Response:

The probability that a student has a pet, given they do not have any siblings is:

Option: D ( 60%)

Step-by-step breakdown:

Let A represent the situation where a student lacks a sibling.

Let B signify the occurrence that a student has a pet.

Consequently, A∩B refers to the event in which a student is without siblings but possesses a pet.

Let P denote the chance of an event happening.

We need to determine:

P(B|A)

From our knowledge:

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

From the data provided:

P(A)=0.25

and P(A∩B)=0.15

Thus,

$P(B|A)=\dfrac{0.15}{0.25}\\\\P(B|A)=\dfrac{3}{5}\\\\P(B|A)=0.6$

which expressed as a percentage is:

$0.6\times 100=60\%$

Therefore, the probability is:

60%

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