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There is a stack of
8
cards, each given a different number from
1
to
8
. Suppose we select a card randomly from the stack, replace it, and then randomly select another card. What is the probability that the first card is an odd number and the second card is greater than
6
?

Respuesta :

shoopdawhoopdedo
Probability you'd pick an odd number:

1 2 3 4 5 6 7 8

Odd numbers: 1 3 5 7
There are 4/8 odd numbers so probability is 4/8 first pick.

Card is put back so you still have 8 cards. Probability greater than 6:
7 and 8 are greater than 6, so that's 2 out of 8 cards. Probability: 2/8

Multiply both probabilities together: 4/8 x 2/8 = 8/64 = 1/8

The probability that the first card is an odd number and the second card is greater than 6 is 1/8.

What is probability?

"Probability means possibility. It is a branch of mathematics that deals with the occurrence of a random event. The value is expressed from zero to one".

For the given situation,

The sample space s = {1, 2, 3, 4, 5, 6, 7, 8}

⇒[tex]n(s)=8[/tex]

Let a be the probability that the first card is an odd number.

a = {1, 3, 5, 7}

Let b be the probability that the second card is greater than 6.

b={7, 8}

The event is the probability that the first card is an odd number and the second card is greater than 6. So,

a ∩ b = {7}

⇒[tex]n(a[/tex] ∩ [tex]b)[/tex] = 1

Thus, P(event) =  n(a∩b)/n(s)

⇒[tex]P(event)=\frac{1}{8}[/tex]

Hence we can conclude that the probability that the first card is an odd number and the second card is greater than 6 is 1/8.

Learn more about probability here

brainly.com/question/13604758

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