review formulas with examples

      review formulas with examples negation: P ( E ) + P ( E  ) = 1 or: P ( A  B ) = P ( A ) + P ( B ) - P ( A  B ) if: P ( A / B ) = and: P ( A  B ) = P ( A ) P ( B / A )      

negation: P ( E ) + P ( E  ) = 1 Roll 3 dice. What is the probability that AT LEAST two land on the same number? next

negation: P ( E ) + P ( E  ) = 1 Roll 3 dice. What is the probability that AT LEAST two land on the same number? S = event that at least 2 same S  = event that all are different If you do NOT have at least 2 landing on the same number then they all land on different numbers. next

negation: P ( E ) + P ( E  ) = 1 Roll 3 dice. What is the probability that AT LEAST two land on the same number? S = event that at least 2 same S  = event that all are different P(S ) = = P(S) = next

negation: P ( E ) + P ( E  ) = 1 Draw 3 marbles without replacement. What is the probability that AT LEAST one is blue? Roll 3 dice. What is the probability that AT LEAST two land on the same number? S = event that at least 2 same S  = event that all are different P(S ) = = P(S) = next

negation: P ( E ) + P ( E  ) = 1 Draw 3 marbles without replacement. What is the probability that AT LEAST one is blue? Roll 3 dice. What is the probability that AT LEAST two land on the same number? B = event that at least 1 is blue S = event that at least 2 same B  = event that all are red S  = event that all are different P(S ) = = If you do NOT have at least one blue then they are all red. P(S) = next

negation: P ( E ) + P ( E  ) = 1 Draw 3 marbles without replacement. What is the probability that AT LEAST one is blue? Roll 3 dice. What is the probability that AT LEAST two land on the same number? B = event that at least 1 is blue S = event that at least 2 same B  = event that all are red S  = event that all are different P(S ) = = P(B ) = = P(S) = P(B) = next

negation: P ( E ) + P ( E  ) = 1 Draw 3 marbles without replacement. What is the probability that AT LEAST one is blue? Roll 3 dice. What is the probability that AT LEAST two land on the same number? B = event that at least 1 is blue S = event that at least 2 same B  = event that all are red S  = event that all are different P(S ) = = P(B ) = = P(S) = P(B) = return to outline

 K  Q  J  K  Q  J  K  Q  J  K  Q  J or: P ( A  B ) = P ( A ) + P ( B ) - P ( A  B ) Draw 2 cards without replacement from the deck pictured above. What is the probability that they are both red or both kings? next

 K  Q  J  K  Q  J  K  Q  J  K  Q  J or: P ( A  B ) = P ( A ) + P ( B ) - P ( A  B ) Draw 2 cards without replacement from the deck pictured above. What is the probability that they are both red or both kings? R = both red P(R) = 6C2 = = 15 = 12C2 = = 66 next

 K  Q  J  K  Q  J  K  Q  J  K  Q  J or: P ( A  B ) = P ( A ) + P ( B ) - P ( A  B ) Draw 2 cards without replacement from the deck pictured above. What is the probability that they are both red or both kings? K = both kings P(K) = R = both red P(R) = = = next

 K  Q  J  K  Q  J  K  Q  J  K  Q  J or: P ( A  B ) = P ( A ) + P ( B ) - P ( A  B ) Draw 2 cards without replacement from the deck pictured above. What is the probability that they are both red or both kings? K = both kings P(K) = R = both red P(R) = = =  K  K R K= one hand There is only 1 pair of cards satisfying: They are both red AND they are both kings. P(R K)= next

 K  Q  J  K  Q  J  K  Q  J  K  Q  J or: P ( A  B ) = P ( A ) + P ( B ) - P ( A  B ) Draw 2 cards without replacement from the deck pictured above. What is the probability that they are both red or both kings? K = both kings P(K) = R = both red P(R) = = =  K  K R K= one hand P ( R  K ) = P ( R ) + P ( K ) - P ( R  K ) - + = P(R K)= next

 K  Q  J  K  Q  J  K  Q  J  K  Q  J or: P ( A  B ) = P ( A ) + P ( B ) - P ( A  B ) Draw 2 cards without replacement from the deck pictured above. What is the probability that they are both red or both kings? K = both kings P(K) = R = both red P(R) = = =  K  K R K= one hand P ( R  K ) = P ( R ) + P ( K ) - P ( R  K ) - + = P(R K)= return to outline

if: P ( A / B ) = In a certain population, 13% are left handed males and 52% are male. A person is selected at random from this population. What is the probability he is left handed IF he is male? = if: P ( L / M ) = next

if: P ( A / B ) = In a certain population, 13% are left handed males and 52% are male. A person is selected at random from this population. What is the probability he is left handed IF he is male? = = .25 if: P ( L / M ) = next

if: P ( A / B ) = In a certain population, 13% are left handed males and 52% are male. A person is selected at random from this population. What is the probability he is left handed IF he is male? = = .25 if: P ( L / M ) = return to outline

 K  Q  J  K  Q  J  K  Q  J  K  Q  J and: P ( A  B ) = P ( A ) P ( B / A ) Draw 2 cards without replacement from the deck pictured above. What is the probability that the first is a heart and the second is a heart? next

 K  Q  J  K  Q  J  K  Q  J  K  Q  J and: P ( A  B ) = P ( A ) P ( B / A ) Draw 2 cards without replacement from the deck pictured above. What is the probability that the first is a heart and the second is a heart? and: P ( R1  R2 ) = P (R1 ) P (R2 / R1 ) next

and: P ( A  B ) = P ( A ) P ( B / A )  Q  J  K  Q  J  K  Q  J  K  Q  J  K Draw 2 cards without replacement from the deck pictured above. What is the probability that the first is a heart and the second is a heart? and: P ( R1  R2 ) = P (R1 ) P (R2 / R1 ) If the first card is a heart: next

and: P ( A  B ) = P ( A ) P ( B / A )  K  Q  J  K  Q  J  K  Q  J  K  Q  J Draw 2 cards without replacement from the deck pictured above. What is the probability that the first is a heart and the second is a heart? and: P ( R1  R2 ) = P (R1 ) P (R2 / R1 ) = return to outline

review formulas with examples