When a quarter is tossed four times, there are the following 16 possible outcome

Question

When a quarter is tossed four times, there are the following 16 possible outcomes. Here, for example, HTTH represents the outcome that the first toss is heads, the next two tosses are tails, and the fourth toss is heads.

a. List the outcomes constituting each of the following three events, then tell me the probability of the event.

A = event all four tosses come up the same

B = event exactly three tails are tossed   

C = event the first toss is tails

b. Which pairs of events are mutually exclusive (if any)? Explain your answer.

c. For each of the following events, describe the event in words and then give the probability of the event.

(B & C)

(B or C)

(not A)   

Explanation / Answer

a)

n(A) = event all four tosses come up the same = {HHHH , TTTT} = 2

n(B) = Total possible outcomes = 16

P(S) = n(A) / n(B) = 2 / 16

n(A) = event exactly three tails are tossed = { HTTT , THTT , TTHT , TTTH } = 4

n(B) = Total possible outcomes = 16

P(S) = n(A) / n(B) = 4 / 16

n(A) = event the first toss is tails = {THHH , THHT , THTH , THTT , TTHH, TTHT , TTTH , TTTH } = 8

n(B) = Total possible outcomes = 16

P(S) = n(A) / n(B) = 8 / 16

b)

Event A and B are mutually exclusive
Because outcome of A are = {HHHH ,TTTT}
Outcome of B are = { HHHT , HHTH , HHTT , HTHH , HTHT , HTTH , HTTT , THHH , THHT , THTH , THTT , TTHH, TTHT , TTTH}
In these two set of outcomes there is no common outcomes.
Hence, these two events are not mutually exclusive.

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