n = 7
P(success) = 0.35
The number of successes among a fixed number of independent trials follows binomial distribution. Lets evaluate the definition of binomial probability at m = 0, 1, 2, 3:
P(X=m)=C(n,m)⋅pm⋅(1−p)n−m P(X=0)=C(7,0)⋅0.350⋅(1−0.35)7−0=0!(7−0)!7!⋅0.350⋅0.657=0.049
P(X=1)=C(7,1)⋅0.351⋅(1−0.35)7−1=1!(7−1)!7!⋅0.351⋅0.656=0.1848
P(X=2)=C(7,2)⋅0.352⋅(1−0.35)7−2=2!(7−2)!7!⋅0.352⋅0.655=0.2985
P(X=3)=C(7,3)⋅0.353⋅(1−0.35)7−3=3!(7−3)!7!⋅0.353⋅0.654=0.2679
P(X<4)=P(X=0)+P(X=1)+P(X=2)+P(X=3)
P(X<4)=0.049+0.1848+0.2985+0.2679=0.8002
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