let X is number of heads which follows binomial distribution with parameter n=7 and p=1/2
P(at most 3 heads)=P(X<=3)=P(X=0)+P(X=1)+P(X=2)+P(X=3)
=7C0(1/2)0(1/2)7+7C1(1/2)1(1/2)6+7C2(1/2)2(1/2)5+7C3(1/2)3(1/2)4
=0.0078+0.0547+0.1641+0.2734=0.5
hence P(1 heads given at most 3 heads)=P(X=1|X<=3)=P(X=1)/P(X<=3)=0.0547/0.5=0.1094
MA 485-585 PROBABILITY THEORY QUIZ #1 JANUARY 22 Time alotted: 15 min. Each question is 10...
MA 485-585 PROBABILITY THEORY QUIZ #1 JANUARY 22 2. An urn contains 7 black and 4 white balls. We randomly draw 4 of the 11 balls What is the probability that we selected exactly 3 black and 1 white balls?
Week#5: Question 1: A team of 10 members, 3 are men and 7 are women. A committee of 4 people will be chosen randomly. What is the probability that the committee will have atleast two men on it? Question 2: In this experiment, you flip a fair coin four times. Make a tree diagram of this experiment. What is the probability that out of four coin tosses, you get exactly two heads in a row?
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