Which statement is true?

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kiaandkeeks kiaandkeeks

28-11-2018
Mathematics

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Which statement is true?

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erato erato · Answer 1 · 2019-04-28T12:33:53+02:00

Answer:

Option: C is the correct answer.

C. Buying a needle and buying thread are dependent events.

Step-by-step explanation:

let A denotes the events of buying a thread.

and B denote the event of buying a needle.

Then A∩B denote the event of buying a needle and a thread.

Also let P denote the probability of an event.

i.e. we are given:

P(A)=0.15

Also P(B|A)=0.25

As we know that:

[tex]P(B|A)=\dfrac{P(A\bigcap B)}{P(A)}\\\\i.e.\\\\0.25=\dfrac{P(A\bigcap B)}{0.15}\\\\i.e.\\\\P(A\bigcap B)=0.0375[/tex]

As we know that when two events A and B are independent then,

P(A∩B)=∅

otherwise they are dependent events.

Hence, option: C is the correct answer.

ardni313 ardni313 · Answer 2 · 2019-10-22T10:39:24+02:00

The true statement are buying a needle and buying thread are dependent events (C)

Further explanation

There are two events in probability:

Independent: each event is not affected by other events

Dependent / Conditional Probability: an event is affected by other events

The notation for probability:

P (A): Probability of A
P (B): Probability of B

for Dependent / Conditional Probability:

P (B | A): Event B given Event A

P (A and B) = P (A) x P (B | A)

P (A and B) = Probability of event A and event B

From the question :

Probability of buying a thread = P (A) = 0.15

The probability that the customer buys a needle is given that the customer bu a thread = P (B | A) = 0.25

So

The probability customers to buy a needle and thread = P (A and B)

= P (A) x P (B | A)

= 0.15 x 0.25

P (A and B) = [tex]\boxed{\bold{0.0375}}[/tex]

It can be concluded that both events are Dependent event

Learn more

a pair of dependent events

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Keywords : probability, dependent events, Independent events