I NEED HELP!
You pick a card at random. Without putting the first card back, you pick a second card at random. There're 3 cards. One is 7, one is 8, and the other is a nine. What is the probability of picking a 7 and then picking a number greater than 7? (Write the probability as a fraction or whole number.)

So, there are 3 cards in total, which means your pobability of picking one card out of the 3 cards is %33.33. So the probability of picking a 7 is 1/3. Because the other two numbers are greater than 7, and you already picked 7 so you cannot pick it again, the probabitily of pick a number greater than 7 is %100, or 3/3.

I hope that answers your question! :)

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ap8997154 ap8997154 · Answer 2 · 2022-01-12T08:39:00+01:00

The probability of picking a 7 and then picking a number greater than 7 is [tex]\dfrac{1}{3}[/tex] or [tex]0.\overline{3}[/tex].

Probability

Probability shows us the chances of an event occurring.

[tex]\bold{Probability =\dfrac{Desired\ Outcome}{Total\ number\ of\ outcomes\ possible}}[/tex]

Now, given that we have already picked three cards. therefore, 7, 8, and 9.

The number of possible outcomes is 3.

the probability of card 7,

[tex]\bold{Probability(7) =\dfrac{Number\ 7(1)}{Total\ number\ of\ outcomes\ possible (3)}= \dfrac{1}{3}}[/tex]

Now, as card seven is already picked up cards 8 and 9 are the only card left.

therefore, the sample size(possible outcomes) was reduced to 2 only.

Also, cards 8 and 9 both are greater than 7, thus the desired outcome is also 2.

Further the probability of the number greater than 7 occurring,

[tex]\bold{Probability(n>7) =\dfrac{cards\ 8\ and\ 9(2)}{Total\ number\ of\ outcomes\ possible (2)}= \dfrac{2}{2} = 1}[/tex]

Probability picking a number greater than 7

The probability of picking a 7 and then picking a number greater than 7

= Probability of card 7 occuring x probability of card 8 and 9 occurring

[tex]=\dfrac{1}{3}\times 1[/tex]

[tex]=\dfrac{1}{3}[/tex]

Hence, the probability of picking a 7 and then picking a number greater than 7 is [tex]\dfrac{1}{3}[/tex] or [tex]0.\overline{3}[/tex].

Learn more about Probability:

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