Probability with Binomial theorem

SECT. 7.7 PROBABILITY WITHTHE BINOMIAL THEOREM

PROBABILITY WITH BINOMIAL THEOREM:

In this section the probability questions will involve only 2outcomes, “A’ and ‘B’

Both events are complimentary:

Ie: True/False, Win/Lose, Odd/Even, Yes/No, Pass/Fail

Ex: The probability that the Canucks will win a game is 64%.What is the probability that they will win 3 out of their next4 games?

List out all the possible outcomes:

W W W L

W W L W

W L W W

L W W W

Calculate the probability of 3 wins

Calculate the probability of 1 Loss

PRACTICE: SUPPOSE A BIASED COIN IS FLIPPED 5 TIMESAND THE P(H) = 0.65. WHAT IS THE PROBABILITY OFGETTING 3 HEADS?

List out all the possible outcomes:

H H H T T

H H T H T

H T H H T

T H H H T

H H T T H

H T H T H

T H H T H

H T T H H

T T H H H

Alternative Method: Combinations

Calculate the probability of 3 heads

Calculate the probability of 2 Tail

T H T H H

PLAYOFF SERIES & “ATLEAST” COMBINATIONS

When solving questions involving playoff series, a best of 5game series means that a team will need to win 3 games towin the series

In addition, a best of 7 game series will require 4 wins

When a team wins a series, the last game they play mustbe a win

Questions involving “atleast” will have multiple scenarios

Sometimes it’s easier to calculate the compliment

THE DALLAS MAVERICKS IS PLAYING A BEST OF 7 GAME SERIESAGAINST THE UTAH JAZZ. THE PROBABILITY THAT THEMAVERICKS WILL WIN A GAME IS 55%. WHAT IS THE PROBABILITYTHAT THEY WILL THE SERIES IN 7 GAMES?

Winning the series in 7 games means that there must be 4 W and 3 L

The last game must be a W, so in 6 games there are 3 W and 3 L

different scenarios

Calculate the probability of 4 wins

Calculate the probability of 3 Losses

PRACTICE: THE PROBABILITY THAT STEVE NASH WILL MAKE AFREE THROW IS 85%. WHAT IS THE PROBABILITY THAT HEWILL MAKE AT LEAST 8 OF HIS NEXT 10 SHOTS?

Need to consider all the scenarios with getting: 8, 9, and 10 shots

There’s 82% that Steve Nash will make at least 8 of his next 10 shots

HOMEWORK: