Chapter 13, Problem 18PT

To determine

Calculate probability of P (even, odd) from 8 cards without replacement.

Answer to Problem 18PT

Probability of finding even and odd numbered card is $\frac{1}{4}$

Explanation of Solution

Given:

Calculations:

Here, we have to calculate probability of finding even and odd numbered card from given data.

Total number of cards=8

Here, 2, 4, 6, 8 are even numbered card that is 4 even cards from total 8 cards. Thus, probability of finding even number card is,

  $P(even)=\frac{4}{8}=\frac{1}{2}$

Here, 1, 3, 5, 7 are odd numbered cards that is 4 odd cards from total 8 cards. Thus, probability of finding odd numbered cards is,

  $P(odd)=\frac{4}{8}=\frac{1}{2}$

Now, probability of finding 5 and odd number cards is,

  $\begin{array}{l}P(even,odd)=P(even)\times P(odd)\\ P(even,odd)=\frac{1}{2}\times \frac{1}{2}\\ P(even,odd)=\frac{1}{4}\end{array}$

Conclusion:

Therefore, we are able to calculate probability of finding even and odd number card from 8 cards.