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You pick a card at random. $\newline$ $3456$ $\newline$ What is $P(\text{not less than } 6)$ ? $\newline$ Write your answer as a percentage. $\newline$ $\_\_\_\_\%$

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Probability of simple events and opposite events

Full solution

Q. You pick a card at random.

\newline

3456

\newline

What is

P(\text{not less than } 6)

?

\newline

Write your answer as a percentage.

\newline

\_\_\_\_\%

Identify total number of cards: Step $1$ : Identify the total number of cards and the relevant cards for the event. $\newline$ In a standard deck, there are $52$ cards. Cards with values less than $6$ are $2$ , $3$ , $4$ , and $5$ of each suit (clubs, diamonds, hearts, spades). Each suit has $4$ cards less than $6$ , so $4$ suits $\times$ $4$ cards $6$ $1$ cards.
Calculate number of cards: Step $2$ : Calculate the number of cards that are not less than $6$ . $\newline$ Total cards = $52$ $\newline$ Cards not less than $6$ = Total cards - Cards less than $6$ $\newline$ = $52 - 16$ $\newline$ = $36$
Calculate probability as percentage: Step $3$ : Calculate the probability as a percentage. $\newline$ Probability (not less than $6$ ) = $(\frac{\text{Number of cards not less than 6}}{\text{Total number of cards}}) \times 100$ $\newline$ = $(\frac{36}{52}) \times 100$ $\newline$ = $69$ . $23$ \%

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