Question

a special deck of cards has ten cards. four are green (g), two are blue (b), and four are red (r). when a card is picked, the color of it is recorded. an experiment consists of first picking a card and then tossing a coin, which lands on heads (h) or tails (t).
part (a)
part (b)
part (c)
let b be the event that a red or green is picked, followed by landing a head on the coin toss. are the events a and b mutually exclusive? explain your answer in one to three complete sentences, including numerical justification
(enter your probability as a fraction.)
a and b are mutually exclusive because they cannot happen at the same time. thus, p(a and b) =

Explanation:

Step1: Understand Mutually Exclusive Events

Mutually exclusive events cannot occur simultaneously, so \( P(A \cap B) = 0 \) if \( A \) and \( B \) are mutually exclusive. We need to confirm if there's any overlap in the outcomes of \( A \) and \( B \). Since they can't happen at the same time, the intersection probability is 0.

Step2: Calculate \( P(A \cap B) \)

For mutually exclusive events, the probability of both occurring is 0. So \( P(A \text{ and } B) = 0 \).

Answer:

\( 0 \)