You pick a card at random. Without putting the first card back, you pick a second card at random. 5 6 7 What is the probability of picking a 7 and then picking a 7? Write your answer as a fraction or whole number. _____

Total Number of Cards: First, we need to determine the total number of cards. Since no specific deck is mentioned, we will assume that the sequence of cards mentioned (5, 6, 7) represents the entire set of cards we are dealing with. Total number of cards = 3 (5, 6, and 7).Probability of First 7: Next, we calculate the probability of picking a 7 on the first draw. Since there is only one 7 in the set of 3 cards, the probability is 1 out of 3. Probability of first 7 = Number of 7s / Total number of cards = 1/3.Probability of Second 7: After picking the first 7, we do not put it back, so there are now only 2 cards left. Since we already picked the 7, there are no 7s left in the set of remaining cards. Therefore, the probability of picking a 7 on the second draw is 0, because there are no 7s left. Probability of second 7 = Number of 7s left / Remaining number of cards = 0/2.Overall Probability: To find the overall probability of both events happening (picking a 7 and then picking another 7), we multiply the probabilities of each individual event. Overall probability = Probability of first 7 * Probability of second 7 = (1/3) * (0/2) = 0.

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You pick a card at random. Without putting the first card back, you pick a second card at random. $\newline$ $5\ 6\ 7$ $\newline$ What is the probability of picking a $7$ and then picking a $7$ ? $\newline$ Write your answer as a fraction or whole number. $\newline$ $\underline{\hspace{3em}}$

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Grade 8

Probability of independent and dependent events

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Q. You pick a card at random. Without putting the first card back, you pick a second card at random.

\newline

5\ 6\ 7

\newline

What is the probability of picking a

7

and then picking a

7

\newline

Write your answer as a fraction or whole number.

\newline

\underline{\hspace{3em}}

Total Number of Cards: First, we need to determine the total number of cards. Since no specific deck is mentioned, we will assume that the sequence of cards mentioned $(5, 6, 7)$ represents the entire set of cards we are dealing with. $\newline$ Total number of cards = $3$ ( $5$ , $6$ , and $7$ ).
Probability of First $7$ : Next, we calculate the probability of picking a $7$ on the first draw. Since there is only one $7$ in the set of $3$ cards, the probability is $1$ out of $3$ .
Probability of first $7$ = Number of $7$ s / Total number of cards = $\frac{1}{3}$ .
Probability of Second $7$ : After picking the first $7$ , we do not put it back, so there are now only $2$ cards left. Since we already picked the $7$ , there are no $7$ s left in the set of remaining cards. Therefore, the probability of picking a $7$ on the second draw is $0$ , because there are no $7$ s left. Probability of second $7 = \frac{\text{Number of 7s left}}{\text{Remaining number of cards}} = \frac{0}{2}.$
Overall Probability: To find the overall probability of both events happening (picking a $7$ and then picking another $7$ ), we multiply the probabilities of each individual event. $\newline$ Overall probability = Probability of first $7$ * Probability of second $7$ = $(1/3) * (0/2) = 0$ .