ACT: Questions

Question: In tossing a fair coin three consecutive times, what is the probability of getting heads on 2 consecutive tosses but NOT on three consecutive tosses? (A fair coin has an equal likelihood of a heads or tails outcome.)

Choices:


	A.		$\frac{1}{4}$
	B.		$\frac{3}{8}$
	C.		$\frac{1}{2}$
	D.		$\frac{5}{8}$
	E.		$\frac{3}{4}$

It pays to think for a minute. How can you have two consecutive heads but not three? Well, the first two tosses could be heads and the third could be tails. Are there any other ways? Yes, the last two tosses could be heads while the first is tails. Those are the only ways to achieve the desired outcome. So what are the probabilities?

For the first desired outcome, you need heads, heads, tails. The

probability of that outcome is:

	1

	2

	1

	2

	1

	2

	1

	8

(There's a one out

of two chance of getting the outcome we want on each toss, so

the chance of getting all three outcomes in a row is:

	1

	2

	1

	2

	1

	2

That's not the answer though. You could also get the tails,

heads, heads outcome. This too has a

	1

	2

	1

	2

	1

	2

	1

	8

probability.

Since either outcome is acceptable, you add the probabilities:

	1

	8

	1

	8

	2

	8

	1

	4

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ACT: Math Question #10