Chapter 13, Problem 19PT

To determine

Calculate probability of P (multiple of 3, multiple of 4) from 8 cards without replacement.

Answer to Problem 19PT

Probability of finding multiple of 3, multiple of 4 numbered cards are $\frac{1}{16}$

Explanation of Solution

Given:

Calculations:

Here, we have to calculate probability of finding multiple of 3, multiple of 4 numbered card from given data.

Total number of cards=8

Here, multiple of 3 from 8 given cards are 3 and 6. It means, there are 2 cards from 8 cards that are multiple of 3.

  $P(multipleof3)=\frac{2}{8}=\frac{1}{4}$

Here, multiple of 4 from 8 given cards are 4 and 8. It means, there are 2 cards from 8 cards that are multiple of 4.

  $P(multipleof4)=\frac{2}{8}=\frac{1}{4}$

Now, probability of finding multiple of 3 and multiple of 4 numbered cards is,

  $\begin{array}{l}P(multipleof3,multipleof4)=P(multipleof3)\times P(multipleof4)\\ =\frac{1}{4}\times \frac{1}{4}\\ =\frac{1}{16}\end{array}$

Conclusion:

Therefore, we are able to calculate probability of finding multiple of 3, multiple of 4 number cards from 8 cards.