Asked Apr 19, 2019


Three fair coins are tossed. The two possible outcomes for a single coin are​ heads, h, and​ tails, t. Complete parts​ (a) through​ (e) below.
​(a) Write out the sample space.
The sample space is?.
​(Use commas to separate answers as​ needed.)
​(b) Determine the probability of no heads.-
​(Type an integer or a simplified​ fraction.)

Expert Answer

Step 1

Part (a):

The sample space is the collection of all outcomes, if a random experiment is performed.

In this case, the random experiment involves tossing 3 fair coins. While writing out the sample space, we shall consider the order; for example, if the first coin shows head, the second coin shows tail and the third coin again shows head, we shall write it as “hth”, according to the notation you have given.

Keeping these in mind, the sample space is: {hhh, hht, hth, htt, thh, tht, tth, ttt}.

Step 2

Part (b):

Observe the sample space. There are total 8 possible outcomes. Out of these, there is only 1 outcome that contains no “h”, that is, no heads: “ttt”.

Now, Probability of an event = (Number of cases favourable to an event) / (T...

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