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There are someredeounters and some white ounters in a bag. At the start, 7 of the counters are red and the rest of the counters are white. Woody takes two counters from the bag. First he takes at random a counter from the bag. He does not put the counter back in the bag. Woody then takes at random another counter from the bag.
(a) Let the number of white counters in the bag be
x,
Draw a tree diagram that represents the above scenario, showing all relevant information.

There are some red counters and some white counters in a bag. At the start, $7$ of the counters are red and the rest of the counters are white. Woody takes two counters from the bag. First he takes at random a counter from the bag. He does not put the counter back in the bag. Woody then takes at random another counter from the bag. $\newline$ (a) Let the number of white counters in the bag be $x$ , $\newline$ Draw a tree diagram that represents the above scenario, showing all relevant information.

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Interpret confidence intervals for population means

Full solution

Q. There are some red counters and some white counters in a bag. At the start,

7

of the counters are red and the rest of the counters are white. Woody takes two counters from the bag. First he takes at random a counter from the bag. He does not put the counter back in the bag. Woody then takes at random another counter from the bag.

\newline

(a) Let the number of white counters in the bag be

x

,

\newline

Draw a tree diagram that represents the above scenario, showing all relevant information.

Define total counters: Step $1$ : Define the total number of counters in the bag. Since we know there are $7$ red counters and $x$ white counters, the total number of counters is $7 + x$ .
Draw first level: Step $2$ : Draw the first level of the tree diagram for the first counter Woody takes. There are two possibilities: taking a red counter or a white counter. The probability of taking a red counter is $\frac{7}{7 + x}$ , and the probability of taking a white counter is $\frac{x}{7 + x}$ .
Draw second level: Step $3$ : Draw the second level of the tree diagram, considering the outcomes of the first draw. If the first counter is red, the remaining counters are $6$ red and $x$ white. The probabilities for the second draw are then $\frac{6}{6 + x}$ for red and $\frac{x}{6 + x}$ for white. If the first counter is white, the remaining counters are $7$ red and $(x-1)$ white. The probabilities for the second draw are then $\frac{7}{7 + x - 1}$ for red and $\frac{x-1}{7 + x - 1}$ for white.
Complete tree diagram: Step $4$ : Complete the tree diagram by labeling each branch with the appropriate probability and outcome. This includes all combinations: red-red, red-white, white-red, and white-white.

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