Question

can some one please help!!? I will fan and medal best answer.

A box contains twenty-five cards numbered 1 through 25. One card is to be randomly drawn from the box.

Answer 1

@jagr2713 @mustafa2014

Answer 2

What's the rest of the question? What probability are we looking for?

Answer 3

sorry. :(
What is the probability that the card drawn will show a multiple of 5, a multiple of 6, or a multiple of 7?

Answer 4

Let \(X\) denote the event that a given card is a multiple of 5, \(Y\) for multiples of 5, and \(Z\) for multiples of 7.

Then
\[\begin{align*}P(X\cup Y\cup Z)&=P(X\cup Y)+P(Z)-P((X\cup Y)\cap Z)\\\\
&=P(X)+P(Y)-P(X\cap Y)+P(Z)-P((X\cup Y)\cap Z)
\end{align*}\]
which means the probability you want is the probability that you get a multiple 5, plus the prob you get a multiple of 6, minus the prob of getting a card that's a multiple of both 5 and 6, plus the prob of a mult of 7, minus the prob of something that's either a mult of 5 or 6 AND 7.

Does that make sense?

Answer 5

Of the cards from 1-25, you have:
Multiples of 5: \(X=\{5, 10, 15, 20, 25\}\)
Multiples of 6: \(Y=\{6,12,18,24\}\)
Multiples of 7: \(Z=\{7,14,21\}\)

As you can see, none of the sets have common elements, so the probabilities of the intersections above are all zero.

Answer 6

so it would be 12/25?

Answer 7

Yep

Answer 8

okay thank you so much for the help. :)

Answer 9

yw