Aim: How do we find the probability with two outcomes?

Do Now: John takes a multiple choice test on a topic for which he has learned nothing. Each question has 3 choices.

a) What is the probability that John answers a question i) correctly? ii) incorrectly?

b) If there are 4 questions on the test what is the probability John answers: i) all questions correctly? ii) only the first 3 questions correctly?

HW: p.699 # 6,7,8,9,11,12,13,14

81

1

3

1

3

1

3

1

3

1

81

2

3

2

3

1

3

1

3

1

Suppose we wanted to know the probability that John answered any 3 questions correctly

but we have to consider the fact that the correct answers can occur in any order (1st ,2nd ,3rd or 1st ,2nd,4th or 1st ,3rd,4th or 2nd,3rd,4th). Therefore, we have to involve the combination.

The answer seems to be the same as Do Now b) ii)

81

2

81

8

81

24

81

234 C

If a fair coin is tossed 10 times what is the probability that it comes up tails exactly 6 times?

To find the probability involving two outcomes, we can use the Bernoulli’s Theorem. rnr

rn qpC

where n = # of trials, r = # of successes, p = probability of success and q = probability of failure. Notice that q = 1 – p

p =1/2 and q = 1/2, n = 10, r = 6

1024

210

16

1

64

1210)2/1()2/1( 46

610 C

The probability that the Wings will win a baseball game is 2/3. What is the probability that they will win:exactly 2 out of 4 games? exactly 3 out of 4 games?

For a certain product, the probability of getting one that is defective is 0.3. If an inspector was to select a product at random find the probability of i) 3 defectives out of 5 selections:ii) 2 defectives out of 5 selections:iii) 4 good products out of 5 selections:iv) 2 defectives out of 6 selections:

a) 24/81

b) 32/81

a) .1323

b) .3087

c) .36015

d) .324135