Question

Which events are independent?Use your intuitive understanding of independence to form an opinion about whether each of the following scenarios represents independent events.

a.The results of consecutive tosses of a coin.

b.The opinions of randomly selected individuals in a pre-election poll.

c.A Major League Baseball player's results in two consecutive at-bats.

d.The amount of gain or loss associated with investments in different stocks if these stocks are bought on the same day and sold on the same day 1 month later.

e.The amount of gain or loss associated with investments in different stocks bought and sold in different time periods, 5 years apart.

f.The prices bid by two different development firms in response to a building construction proposal.

Short answer

1. Event A is independent.
2. Event B is independent.
3. Event C is independent.
4. Event D is not independent.
5. Event E is independent.
6. The event F is not independent.

Step-by-step solution

(a) The results of consecutive tosses of a coin

To the data, some flip of a coin does not produce another flip of a coin event. So, event A is independent.

(b) The opinions of randomly selected individuals in a pre-election poll

Based on the facts, the view of a randomly picked person together in a pre-election study probably does not impact someone person's current view. Hence, event B is independent.

(c) A Major League Baseball player's results in two consecutive at-bats

A. To data, the result of such discussion does not affect something else's occurrence. Accordingly, event C is independent.

(d) The amount of gain or loss associated with investments in different stocks if these stocks are bought on the same day and sold on the same day 1 month later

A. To data because of this the earnings or losses in respect of investments in various equities purchased the same day. They offered one month ago and are expected to be substantially connected. Hence, event D is not independent.

(e) The amount of gain or loss associated with investments in different stocks that are bought and sold in different time periods, 5 years apart

A. To the data, because occurrences eventuate 5 years separately that is improbable that some stock's bought and sold will influence the purchase and offer from another firm. So, event E is independent.

(f) The prices bid by two different development firms in response to a building construction proposal

Since each developer as the data cannot decide the proposition. So, the event F is not independent. Therefore, event F is not independent.