Math CentralQuandaries & Queries


Question from Atina:

A spinner has four equal sectors and a number is written on each sector; 1, 2, 3 and 4. A two-digit number is formed by spinning two times. The number on the first spinning makes the first digit and the number on the second spinning makes the second digit. For example, 2 on the first spinning and 1 on the second spinning make the number 21.
(a) Give the sample space S for the experiment.
(b) Consider the following events : E = odd number; F = number smaller than 35; G = prime number.
Give the subset of outcomes in S that defines each of the events E, F, and G.
(c) Describe the following events in terms of E, F, and G and find the probabilities for the events.
• getting an even integer less than 35.
• getting an odd number or an prime.
• getting an even number greater than or equal to 35 that is a prime number. • an odd number smaller than 35 that is not a prime number.
(d) Are E and F mutually exclusive events? Give a reason for your answer.

Hi Atina,

I can help get you started.

On any two-spins of the spinner you can obtain 1 to 4 as the first (tens) digit and 1 to 4 as the second (units) digit. Thus you resulting two-digit number can be any one of

11, 12, 13, 14, 21, ... 24, 31,..., 41, ... 44

This is the sample space and contains 16 elements.

Since any single spin yields 1 to 4, equally likely, any of the 16 possible outcomes in the sample space are equally likely.

For the first bullet in part (c) you want outcomes that are not in $E$ but are in $F.$ The sample space is $S$ so I would write the elements not in $E$ as $S - E.$ Your textbook or teacher may use some other notation. So for this bullet you want the outcomes in $S - E$ and in $F.$ This is the intersection of $S - E$ and $F$ which I would write $(S - E) \cap F.$


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