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
Then, this event
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.
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Probability of at least 2 boys = P[(2 boys & 3 girls) + (3 boys & 2 girls) + (4 boys & 1 girl) + (5 boys & 0 girl)]
Explanation:
p2boys&3girls=C(5,2)×(C(10,3))(C(15,5))
=10×1203003=12003003=0.3996
p3boys&2girls=C(5,3)×(C(10,2))(C(15,5))
=10×453003=4503003=0.1498
p4boys&1girl=C(5,4)×(C(10,1))(C(15,5))
=5×103003=503003=0.0166
p5boys&0girl=C(5,5)×(C(10,0))(C(15,5))
=1×13003=13003=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