1.Consider the experiment of flipping a fair coin 4 consecutive times. Let H rep

Question

1.Consider the experiment of flipping a fair coin 4 consecutive times. Let H represent“heads”, and T represent “tails”.

(a) Write out the sample space for this experiment. How many elements are in the sample space?

(b) Using the sample space in (a), what is the probability of flipping exactly 2 heads in this experiment? What is the probability of flipping at least 2 tails?

2. Repeat # 1, but this time with 100 flips of a fair coin. Is it feasible to write out the sample space? Explain. Calculate the requested probabilities using counting principles only.

Explanation / Answer

1 a) Sample Space S = {HHHH, HHHT, HHTH, HTHH, THHH, HHTT, HTTH, TTHH, HTHT, THTH, THHT, TTTH, TTHT, THTT, HTTT, TTTT}

b) P(exactly 2 heads) = 6/16 = 3/8

P(at least 2 tails) = P(2 tails) + P(3 tails) + P(4 tails)

= (6+ 4 +1)/16

= 11/16

2 a) Total elemets in sample space = 2100

So, it is not feasible to write sample space

b) P(exactly 2 heads) = 100C2/2100

= 3.9x10-27

P(at least 2 tails) = 1 - P(0 tails) - P(1 tail)

= 1 - (1/2)100 - 100x(1/2)100

= 1

Related Questions

Navigate

• Browse (All)
• Browse 1
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.