Question

an experiment consists of first rolling a die and then tossing a coin: a. how many elements are there in the sample space? b. let a be the event that either a 1, 2, 3 or 4 is rolled first, followed by landing a tail on the coin toss. p(a) = present your answer as a decimal rounded to four decimal places. c. let b be the event that an even number is rolled, followed by landing a tail on the coin toss. are the events a and b mutually exclusive? yes, they are mutually exclusive no, they are not mutually exclusive hint: mutually exclusive video on probability +

Explanation:

Step1: Calculate sample - space size

The die has 6 possible outcomes and the coin has 2 possible outcomes. By the multiplication principle, the number of elements in the sample space $n(S)=6\times2 = 12$.

Step2: Calculate $P(A)$

The event $A$: rolling a 1, 2, 3, or 4 on the die and then getting a tail on the coin. There are 4 possible outcomes for the die roll and 1 possible outcome (tail) for the coin toss. So $n(A)=4\times1 = 4$. Then $P(A)=\frac{n(A)}{n(S)}=\frac{4}{12}\approx0.3333$.

Step3: Determine mutual - exclusivity

Event $A$: { (1, T), (2, T), (3, T), (4, T) }. Event $B$: { (2, T), (4, T), (6, T) }. Since $A\cap B=\{(2, T),(4, T)\}
eq\varnothing$, events $A$ and $B$ are not mutually exclusive.

Answer:

a. 12
b. 0.3333
c. No, they are not Mutually Exclusive