In a college 35% students are girls. Find the probability that: (i) t

1.	In a college 35% students are girls. Find the probability that: (i) two are girls, (ii) at least one is a girl in a random sample of 5 students.
Answer» Let x be the number of girls is a binomial variate with the parameters n-5,p = 0.35 and p = 1 -P = 1 – 0.35 = 0.65. Then the p is: p(x) = nc_xp^xq^{n – x}; x = 0,1,2, …… n = 5c_x (0.35)^x (0.65)^5-x; x = 0,1,2, …….. 5 (i) p( girls ) =p(x = 2) = = 5c₂ (0.35)² (0.65)^{5 – 2} = 10 x 0.1225 x 0.2746 = 0.3364 (ii) p(at least one is a girl) = p(x > 1) = 1 – p (x < 1) = 1 – p (x = 0) = 1 -5C₀(0.35)⁰(0.65)^{5 – 0} = 1 – [1 x 1 x 0.1160] = 0.884

In a college 35% students are girls. Find the probability that: (i) two are girls, (ii) at least one is a girl in a random sample of 5 students.

Answer»

Let x be the number of girls is a binomial variate with the parameters n-5,p = 0.35 and
p = 1 -P
= 1 – 0.35 = 0.65.
Then the p is:
p(x) = nc_xp^xq^{n – x}; x = 0,1,2, …… n
= 5c_x (0.35)^x (0.65)^5-x; x = 0,1,2, …….. 5
(i) p( girls ) =p(x = 2) = = 5c₂ (0.35)² (0.65)^{5 – 2}

= 10 x 0.1225 x 0.2746 = 0.3364
(ii) p(at least one is a girl) = p(x > 1)

= 1 – p (x < 1) = 1 – p (x = 0)
= 1 -5C₀(0.35)⁰(0.65)^{5 – 0}

= 1 – [1 x 1 x 0.1160] = 0.884

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In a college 35% students are girls. Find the probability that: (i) two are girls, (ii) at least one is a girl in a random sample of 5 students.

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