### Probability Review

Hi everyone this is what we did in first class of am. Mr Explained how to use the fundamental principle of counting, formulas that deals with factorial. They seem hard at the beginning, but they get easy as you go along and do them. The question were as follows:

first question:

there are 9 people on a baseball team and they are selecting people to play the different positions.

a) how many ways can the position be filled if there are no restrictions on who plays which position?

answer: 9!= 362880

b) what is the probability that AL is the pitcher if the other positions are selected randomly?

answer: P(AL is the pitcher)

=1*8/9!

=8!/9*8!

=1/9

c) what is the probability that AL, BOB, or CAL are selected to be pitcher if all positions are selected randomly?

answer: 3*8!/9!

=3/9=1/3

d) what is the probability that AL, BOB or CAL are pitcher and DAN or ED are catcher if all positions are selected randomly?

p ( DAN or ED are catcher) = 2*7!/9! = 2/9*8= 1/36

P(d)= 3*2*7!/9!

= 3*2!/9*8!

=1/12

second question:

the probability that GALLANT fox will win the 1st race is 2/5 and that NASHAV will win the 2nd race is 1/3

a) what is the probability that both horses win their races?

P (both win) 2/5 * 1/3= 2/5

b) what is the probability that both horses lose their races?

P(both lose)= 3/5* 2/3= 2/5

c) what is the probability that at least one horse will win its race?

all possible outcomes:

G-W N-L

G-L N-W

G-W N-W

G-L N-L

p (at least one win)= 1-2/5 (p both lose) = 3/5

then mr.K did some extra example where he had to divide the class into boys and girls. he used a new words. that he explained ie. mutual exclusive which means if one way happens there is no way the other can happen.

examples as follows:

P (boy)= 14/20

P ( girl)= 6/20

P 9(blond=1/20

p ( girl or blond) = p ( g) p (bl) = 6/20 + 1/20

p ( boy or blond) = p ( b) + p ( bl)= 14/20 + 1/20

p (A or B) = P (a) + p ( b) - P ( anb) = 15/20 -1/20= 14/20.

do pages 31 and 37 odd #'s 1-9 for homework. mr.k said we going to have p. test on thursday second class.

thats all folks. i am going to post the notes around 11 pm. just because i am at work know, and my break is almost over. sorry guys i know you got to go to bed by 10pm.

first question:

there are 9 people on a baseball team and they are selecting people to play the different positions.

a) how many ways can the position be filled if there are no restrictions on who plays which position?

answer: 9!= 362880

b) what is the probability that AL is the pitcher if the other positions are selected randomly?

answer: P(AL is the pitcher)

=1*8/9!

=8!/9*8!

=1/9

c) what is the probability that AL, BOB, or CAL are selected to be pitcher if all positions are selected randomly?

answer: 3*8!/9!

=3/9=1/3

d) what is the probability that AL, BOB or CAL are pitcher and DAN or ED are catcher if all positions are selected randomly?

p ( DAN or ED are catcher) = 2*7!/9! = 2/9*8= 1/36

P(d)= 3*2*7!/9!

= 3*2!/9*8!

=1/12

second question:

the probability that GALLANT fox will win the 1st race is 2/5 and that NASHAV will win the 2nd race is 1/3

a) what is the probability that both horses win their races?

P (both win) 2/5 * 1/3= 2/5

b) what is the probability that both horses lose their races?

P(both lose)= 3/5* 2/3= 2/5

c) what is the probability that at least one horse will win its race?

all possible outcomes:

G-W N-L

G-L N-W

G-W N-W

G-L N-L

p (at least one win)= 1-2/5 (p both lose) = 3/5

then mr.K did some extra example where he had to divide the class into boys and girls. he used a new words. that he explained ie. mutual exclusive which means if one way happens there is no way the other can happen.

examples as follows:

P (boy)= 14/20

P ( girl)= 6/20

P 9(blond=1/20

p ( girl or blond) = p ( g) p (bl) = 6/20 + 1/20

p ( boy or blond) = p ( b) + p ( bl)= 14/20 + 1/20

p (A or B) = P (a) + p ( b) - P ( anb) = 15/20 -1/20= 14/20.

do pages 31 and 37 odd #'s 1-9 for homework. mr.k said we going to have p. test on thursday second class.

thats all folks. i am going to post the notes around 11 pm. just because i am at work know, and my break is almost over. sorry guys i know you got to go to bed by 10pm.

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