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There are $7$ red and $3$ blue balls in the box. $5$ balls are randomly drawn from the box. What is the probability of the event \

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Convert between customary and metric systems

Full solution

Q. There are

7

red and

3

blue balls in the box.

5

balls are randomly drawn from the box. What is the probability of the event \

Calculate Total Ways: Calculate the total number of ways to draw $5$ balls from the box. $\newline$ Total balls = $7$ red + $3$ blue = $10$ balls. $\newline$ Number of ways to choose $5$ balls from $10$ = $10C5 = 252$ .
Calculate Favorable Outcomes: Calculate the number of favorable outcomes for drawing no more than $2$ red balls. $\newline$ - Ways to draw $0$ red balls (all blue): $3C5 = 0$ (since we can't draw $5$ balls from $3$ ). $\newline$ - Ways to draw $1$ red ball: $7C1 \times 3C4 = 7 \times 0 = 0$ (can't draw $4$ balls from $3$ ). $\newline$ - Ways to draw $2$ red balls: $7C2 \times 3C3 = 21 \times 1 = 21$ . $\newline$ Total favorable outcomes = $0 + 0 + 21 = 21$ .
Calculate Probability: Calculate the probability. $\newline$ Probability = Favorable outcomes / Total outcomes = $\frac{21}{252}$ . $\newline$ Simplify the fraction = $\frac{1}{12}$ .

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