Problem 40BSC

Probability from a Sample Space. In Exercise, use the given sample space or construct the required sample space to find the indicated probability.

Three Children Use this sample space listing the eight simple events that are possible when a couple has three children (as in Example 1): {bbb, bbg, bgb, bgg, gbb, gbg, ggb, ggg}. Assume that boys and girls are equally likely, so that the eight simple events are equally likely. Find the probability that when a couple has three children, there is exactly one girl.

Florida Lottery Let A denote the event of placing a $1 straight bet on the Florida Play 4 lottery and winning. The chance of event A occurring is 1 in 10,000. What is the value of P (A)? What is the value of P (Ā)?

Four Children Exercise lists the sample space for a couple having three children. First identify the sample space for a couple having four children, then find the probability of getting three girls and one boy (in any order).

Example 1 In the following display, we use "b" to denote a baby boy and "g" to denote a baby girl.

Procedure |
Example of Event |
Sample Space(List of Simple Events) |

Single birth |
1 girl (simple event) |
{b, g} |

3 births |
2 boys and 1 girl (bbg, bgb, and gbb are all simple events resulting in 2 boys and 1 girl) |
{bbb, bbg, bgb, bgg, gbb, gbg, ggb, ggg} |

With one birth, the result of 1 female is a simple event because it cannot be broken down any further. With three births, the event of "2 girls and 1 boy" is not a simple event because it can be broken down into simpler events, such as ggb, gbg, or bgg. With three births, the sample space consists of the eight simple events listed above. With three births, the outcome of ggb is considered a simple event, because it is an outcome that cannot be broken down any further. We might incorrectly think that ggb can be further broken down into the individual results of g, g, and b, but g, g, and b are not individual outcomes from three births. With three births, there are exactly eight outcomes that are simple events: bbb, bbg, bgb, bgg, gbb, gbg, ggb, and ggg.

Answer:

Step 1 of 1

Sample space for a couple having four children

Here the sample space consists of {bbbb, bbbg, bbgb, bbgg, bgbb, bgbg, bggb, bggg, gbbb, gbbg, gbgb, gbgg, ggbb, ggbg, gggb, gggg}.

The probability of getting three girls and one boy is

Probability =

=

= 0.25.