Question

A coin is tossed 11 times. a) How many different outcomes are possible? b) How many different outcomes have exactly 8 heads? c) How many different outcomes have at least 2 heads ? d) How many different outcomes have at most 7 heads?

Answer 1

Answer:

a) 2048

b)164

c)54

d) 11

Step-by-step explanation:

a) A coin has two faces.

Outcome possible =2^11= 2048

b) 8 heads possible outcome = 11!/8!3! = 3971688/241/920= 164 ways

c)2 heads outcome= 11!/2!8!= 39716800/725760=54

d) 7 heads= 11!/7!6! =39716800/3628800 = 11

Answer 2

Answer:

2048, 165, 2036, 1816,

Step-by-step explanation:

1. total number of different outcomes for 11 times toss=

$2^{11} = 2048$

2. exactly 8 heads can be found by combination ( exactly n heads possiblity can be found by 11Cn

$11C8 = \frac{11!}{8!(11-8)!}$ = 165

3. number of outcomes with atleast 2 heads can be found by subtracting number of outcomes with with 0 and 1 heads from total number of outcomes

= total number of outcomes - outcomes with 0 heads - outcomes with 1 heads

=  $2^{11} - 11C0 - 11C1$

= 2036

4. number of outcomes with atmost 7 heads can be found by subtracting number of outcomes with  8, 9, 10, 11 heads from total number of outcomes

= total number of outcomes - outcomes with 8 heads - outcomes with  9 heads - outcomes with  10 heads -outcomes with  11 heads

=$2^{11} - 11C8 - 11C9 - 11C10 - 11C11$

=1816