IITM BS Question 5 - Week 6 Practice

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IITM BS Question 5 - Week 6 Practice | Prasnya

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Q5Numerical4 Marks3 Sep 2023

A quiz team of 5 students is to be chosen from a class of 6 boys and 4 girls. Find the probability that there is exactly 3 girls in the team out of the selected 5 students. (Enter the answer correct to 2 decimal places.) The number of ways to choose 5 students from 10 is:

\binom{10}{5}

= 252. We want to select exactly 3 girls (which implies exactly 2 boys). The number of ways to do this is: - Choosing 3 girls from 4:

\binom{4}{3}

= 4 - Choosing 2 boys from 6:

\binom{6}{2}

= 15 Total successful outcomes =

\binom{4}{3} \cdot \binom{6}{2}

= 4 * 15 = 60. The probability is: P =

\frac{60}{252} = \frac{5}{21}

≈ 0.2381. Rounding to 2 decimal places, we get 0.24 (accepted range: 0.21 to 0.27).

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3 Sep 2023

Statistics 1 · Week 6

Q5.A quiz team of 5 students is to be chosen from a class of 6 boys and 4 girls. Find the probability that there is exactly 3 girls in the team out of the selected 5 students. (Enter the answer correct to 2 decimal places.) The number of ways to choose 5 students from 10 is:

\binom{10}{5}

= 252. We want to select exactly 3 girls (which implies exactly 2 boys). The number of ways to do this is: - Choosing 3 girls from 4:

\binom{4}{3}

= 4 - Choosing 2 boys from 6:

\binom{6}{2}

= 15 Total successful outcomes =

\binom{4}{3} \cdot \binom{6}{2}

= 4 * 15 = 60. The probability is: P =

\frac{60}{252} = \frac{5}{21}

≈ 0.2381. Rounding to 2 decimal places, we get 0.24 (accepted range: 0.21 to 0.27).

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