Question

Let the experiment be the toss of six coins in a row. Let X be number of of coins that turn up heads. Determine whether the following statement is true or false: The event that X<3 and the event that X>3 are independent. Question 3 options: True False

Answer 1

True

Explanation:

When a coin is tossed six coins in a row, there are a total of
`2^6` outcomes.

The possible number of times for a heads are {0, 1, 2, 3, 4, 5, 6}.

Let our random variable, Number of coins that turn up heads be X

X={0, 1, 2, 3, 4, 5, 6}.

The event that X<3 and the event that X>3 cannot occur simultaneously in the same outcome.

In an outcome, its either one of the following happens:

• Number of heads = Number of Tails =3
• Number of heads < Number of Tails
• Number of heads > Number of Tails
• Number of heads cannot be greater than Number of Heads

Therefore, the events that X<3 and X>3 are independent.