Chapter 13, Problem 20PT

To determine

Calculate probability of P (5, odd) from 8 cards without replacement.

Answer to Problem 20PT

Probability of finding 5 and odd numbered card is $\frac{1}{16}$

Explanation of Solution

Given:

Calculations:

Here, we have to calculate probability of finding 5 and odd numbered card from given data.

Total number of cards=8

Thus, probability of finding 5 is,

  $P(5)=\frac{1}{8}$

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,

  $\begin{array}{l}P(5,odd)=P(5)\times P(odd)\\ P(5,odd)=\frac{1}{8}\times \frac{1}{2}\\ P(5,odd)=\frac{1}{16}\end{array}$

Conclusion:

Therefore, we are able to calculate probability of finding 5 and odd number card from 8 cards.