Question

Which statement is true?

Answer 1

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) = $\boxed{\bold{0.0375}}$

It can be concluded that both events are Dependent event

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Keywords : probability, dependent events, Independent events

Answer 2

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:

$P(B|A)=\dfrac{P(A\bigcap B)}{P(A)}\\\\i.e.\\\\0.25=\dfrac{P(A\bigcap B)}{0.15}\\\\i.e.\\\\P(A\bigcap B)=0.0375$

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.