Conditional Probability problems
1. Stanford publishes statistics on the SAT scores of their admitted students. In general Stanford admits
10% of the people who apply. Among the people who apply to Stanford about 50% have higher math SAT
scores than verbal SAT scores. Among the people who are admitted to Stanford, 60% have higher math
SAT than verbal SAT scores. If you apply to Stanford with higher math athn verbal SAT scores, what is
the probability you will be admitted?
2. Mario took a survey on campus of girls’ eye colors and their mothers’ eye colors. He found 50 brown
eyed girls who had brown eyed moms. He found 20 brown eyed girls with moms whose eyes were not
brown. He found 10 girls whose eyes were not brown with brown eyed mothers, and 20 whose eyes were
not brown with mothers whose eyes were not brown. Based on this sample evidence, what is the
probability that a girl will have brown eyes given her mother does not have brown eyes? What is the
probability that a mom will not have brown eyes given the girl (her daughter) does not have brown eyes?
3. Josiah did not have enough fertilizer to give to all 100 of the tulip bulbs last fall, so he planted some
with fertilizer and some without. 80 of the plants bloomed. Jay checked the blooming plants and 48 of
them had received fertilizer. Jay checked the non blooming plants and 8 had not received fertilizer. What
is the probability that a plant will bloom, given it was fertilized? What is the probability a plant will bloom
given it was not fertilized?
4. Devin is a great hitter, but sometimes he reacts a little bit to pressure. His lead off hitting percentage is
.350 When he makes an out at his first at bat in the game, his hitting percentage for his second at bat is
.275, but when he make a hit at his first at bat, his hitting percentage for his second at bat is .400. What is
the probability that Devin will get two hits in his first two at bats? One day you got to the game late and
saw Devin get a hit in his second at bat. What is the probability he also had a hit in his first at bat?
Conditional Probability problems
1. Stanford publishes statistics on the SAT scores of their admitted students. In general Stanford admits
10% of the people who apply. Among the people who apply to Stanford about 50% have higher math SAT
scores than verbal SAT scores. Among the people who are admitted to Stanford, 60% have higher math
SAT than verbal SAT scores. If you apply to Stanford with higher math athn verbal SAT scores, what is
the probability you will be admitted?
2. Mario took a survey on campus of girls’ eye colors and their mothers’ eye colors. He found 50 brown
eyed girls who had brown eyed moms. He found 20 brown eyed girls with moms whose eyes were not
brown. He found 10 girls whose eyes were not brown with brown eyed mothers, and 20 whose eyes were
not brown with mothers whose eyes were not brown. Based on this sample evidence, what is the
probability that a girl will have brown eyes given her mother does not have brown eyes? What is the
probability that a mom will not have brown eyes given the girl (her daughter) does not have brown eyes?
3. Josiah did not have enough fertilizer to give to all of the tulip bulbs last fall, so he planted some with
fertilizer and some without. 80 of the plants bloomed. Jay checked the blooming plants and 48 of them
had received fertilizer. Jay checked the non blooming plants and 8 had not received fertilizer. What is the
probability that a plant will bloom, given it was fertilized? What is the probability a plant will bloom given
it was not fertilized?
4. Devin is a great hitter, but sometimes he reacts a little bit to pressure. His hitting percentage is .350
When he makes an out at his first at bat in the game, his hitting percentage for his second at bat is .275, but
when he make a hit at his first at bat, his hitting percentage for his second at bat is .400. What is the
probability that Devin will get two hits in his first two at bats? One day you got to the game late and saw
Devin get a hit in his second at bat. What is the probability he also had a hit in his first at bat?