Question

1. are the events \airline b\ and \30 minutes to 1 hour late\ independent?
2. which of the following is an example of mutually exclusive events?

a. rolling a number cube and getting a 3 and then rolling a 5 on the second roll.
b. drawing a red card from a deck and drawing a king from the same deck.
c. rolling a number cube and getting an even number and getting a prime number.
d. rolling a die and getting 5 and then rolling and odd number on the second roll.

1. two events a and b are independent if:

a. they cannot occur at the same time.
b. the occurrence of one does not affect the probability of the other.
c. the sum of their probabilities is equal to 1.
d. the probability of both occurring is 0.

1. if events a and b are mutually exclusive, then:

a. ( p(a \text{ or } b) = p(a) + p(b) )
b. ( p(a \text{ and } b) = p(a) \times p(b) )
c. ( p(a \text{ or } b) = p(a) + p(b) - p(a \text{ and } b) )
d. ( p(a \text{ and } b) = 1 )

1. the probability of an event happening and the probability of its complement event happening must:

a. be independent.
b. be mutually exclusive.
c. sum to 1.
d. be equal.

1. consider the events of rolling a 6 on a single die and then rolling a 6 on a second roll. these events are:

a. mutually exclusive
b. independent
c. dependent
d. complementary

1. if ( p(a) = 0.4, p(b) = 0.3 ), and ( p(a \text{ and } b) = 0.1 ), what is the probability of a or b occurring?

a. 0.12
b. 0.6
c. 0.7
d. 0.8

1. which of the following is an example of complementary events?

a. rolling a 1 and rolling a 2 on a single die.
b. drawing a heart and drawing a spade from a deck of cards.
c. getting a sum of 7 and getting a sum of 12 when rolling two dice.
d. getting an even number and getting an odd number when rolling a single die.

Explanation:

Step1: Recall the formula for \(P(A\ or\ B)\)

The formula for the probability of the union of two events \(A\) and \(B\) is \(P(A\ or\ B)=P(A)+P(B)-P(A\ and\ B)\).

Step2: Substitute the given values

Given \(P(A) = 0.4\), \(P(B)=0.3\), and \(P(A\ and\ B)=0.1\). Substitute these into the formula:
\(P(A\ or\ B)=0.4 + 0.3-0.1\)

Step3: Calculate the result

\(0.4+0.3 = 0.7\), then \(0.7-0.1=0.6\)

Answer:

b. \(0.6\)