# There are 15 students. 5 of them are boys and 10 of them are girls. If 5 students are chosen, what is the probability that there are at least 2 boys?

##### 2 Answers

Reqd. Prob.

#### Explanation:

let **at least**

Then, this event **mutually exclusive** cases :=

Case (1) :

Exactly

Case (2) :=

Exactly

No. of ways

Case (3) :=

Exactly

Case (4) :=

Exactly

Therefore, total no. of outcomes favourable to the occurrence of the event

Finally,

Hence, the Reqd. Prob.

Enjoy Maths.!

Probability of at least 2 boys = P[(2 boys & 3 girls) + (3 boys & 2 girls) + (4 boys & 1 girl) + (5 boys & 0 girl)]

#### Explanation:

#p_(2 boys &3 girls) = (C(5,2)xx(C(10,3)))/((C(15,5))#

#=(10xx120)/3003=1200/3003=0.3996#

#p_(3 boys &2 girls) = (C(5,3)xx(C(10,2)))/((C(15,5))#

#=(10xx45)/3003=450/3003=0.1498#

#p_(4 boys &1 girl) = (C(5,4)xx(C(10,1)))/((C(15,5))#

#=(5xx10)/3003=50/3003=0.0166#

#p_(5 boys &0 girl) = (C(5,5)xx(C(10,0)))/((C(15,5))#

#=(1xx1)/3003=1/3003=0.0003#

Probability of at least 2 boys = P[(2 boys & 3 girls) + (3 boys & 2 girls) + (4 boys & 1 girl) + (5 boys & 0 girl)]

#=0.3996 + 0.1498+0.0166+0.0003=0.5663#