Answer:
The indicated probability of ![P(D \cup F')=\frac{25}{26}](https://tex.z-dn.net/?f=P%28D%20%5Ccup%20F%27%29%3D%5Cfrac%7B25%7D%7B26%7D)
Step-by-step explanation:
Probability of an event E to be;
P(E) = ![\frac{Number of events within E}{Total number of possible outcomes}](https://tex.z-dn.net/?f=%5Cfrac%7BNumber%20of%20events%20within%20E%7D%7BTotal%20number%20of%20possible%20outcomes%7D)
As per the given condition:
Total number of possible outcomes = 52 cards.
Let the event be D and F as follows;
D : Drawn card is a black card
F : Drawn card is a 10 card.
Then,
From the given condition:
P(D) =
[Out of 52 cards, 26 were black] ,
P(F) =
[Out of 52 cards, there are four 10 cards]
For any two events A and B we always have;
![P(A \cup B) = P(A)+P(B)-P(A \cap B)](https://tex.z-dn.net/?f=P%28A%20%5Ccup%20B%29%20%3D%20P%28A%29%2BP%28B%29-P%28A%20%5Ccap%20B%29)
Now, we have to find the indicated probability:
......[1]
First find the P(F');
P(F') =1-P(F) =
Also, to find
.
We use the formula :
For any event A and B independent variable.
![P(A \cap B) =P(A) \cdot P(B)](https://tex.z-dn.net/?f=P%28A%20%5Ccap%20B%29%20%3DP%28A%29%20%5Ccdot%20P%28B%29)
then;
Now, substitute these in [1];
=![\frac{26+48-24}{52} =\frac{50}{52} = \frac{25}{26}](https://tex.z-dn.net/?f=%5Cfrac%7B26%2B48-24%7D%7B52%7D%20%3D%5Cfrac%7B50%7D%7B52%7D%20%3D%20%5Cfrac%7B25%7D%7B26%7D)
Therefore, the probability of ![P(D \cup F')=\frac{25}{26}](https://tex.z-dn.net/?f=P%28D%20%5Ccup%20F%27%29%3D%5Cfrac%7B25%7D%7B26%7D)