question 24 of 35 step 1 of 1\na box of jerseys for a pick - up game of basketball contains 8 extra - large…
question 24 of 35 step 1 of 1\na box of jerseys for a pick - up game of basketball contains 8 extra - large jerseys, 6 large jerseys, and 5 medium jerseys. if you are first to the box and grab 3 jerseys, what is the probability that you randomly grab 3 large jerseys? express your answer as a fraction in lowest terms or a decimal rounded to the nearest millionth.\nanswerhow to enter your answer (opens in new window) 2 points\nkeypad\nkeyboard shortcuts
Answer
Explanation:
Step1: Calculate the total number of jerseys
The total number of jerseys is (8 + 6+5=19).
Step2: Calculate the number of ways to choose 3 jerseys from 19
Use the combination formula (C(n,r)=\frac{n!}{r!(n - r)!}), where (n = 19) and (r = 3). [ \begin{align*} C(19,3)&=\frac{19!}{3!(19 - 3)!}\ &=\frac{19\times18\times17}{3\times2\times1}\ &=969 \end{align*} ]
Step3: Calculate the number of ways to choose 3 large jerseys from 6
Use the combination formula with (n = 6) and (r = 3). [ \begin{align*} C(6,3)&=\frac{6!}{3!(6 - 3)!}\ &=\frac{6\times5\times4}{3\times2\times1}\ &=20 \end{align*} ]
Step4: Calculate the probability
The probability (P) is the number of favorable outcomes (choosing 3 large jerseys) divided by the number of total outcomes (choosing 3 jerseys). So (P=\frac{C(6,3)}{C(19,3)}). Substitute the values: (P=\frac{20}{969}\approx0.02064)
Answer:
The probability is (\frac{20}{969}\approx0.02064)