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You pick a card at random. $\newline$ $789$ $\newline$ What is $P(\text{not less than } 8)$ ? $\newline$ Write your answer as a fraction or whole number. $\newline$ $\_\_\_\_\_$

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Probability of simple events and opposite events

Full solution

Q. You pick a card at random.

\newline

789

\newline

What is

P(\text{not less than } 8)

?

\newline

Write your answer as a fraction or whole number.

\newline

\_\_\_\_\_

Calculate Total Outcomes: First, let's figure out the total number of possible outcomes when picking a card. Since the problem doesn't specify the type of cards, let's assume a standard deck of $52$ cards.
Count Cards Not Less Than $8$ : Next, we need to count how many cards have a number not less than $8$ . In a standard deck, these would be $8$ , $9$ , $10$ , Jack, Queen, King, and Ace from each suit. That's $7$ cards per suit, and there are $4$ suits. So, $7$ cards $\times$ $4$ suits $= 28$ cards.
Calculate Probability: Now, calculate the probability. Probability = $\frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}} = \frac{28}{52}$ .
Simplify Fraction: Simplify the fraction $\frac{28}{52}$ . Both numbers are divisible by $4$ . So, $28 \div 4 = 7$ and $52 \div 4 = 13$ . Therefore, the simplified fraction is $\frac{7}{13}$ .

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