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?

2048, 165, 2036, 1816,

Step-by-step explanation:

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

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

= 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

=  

= 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

=

=1816

answer: the answer is one of

step-by-step explanation:   we are given to write a proper fraction where the whole is divided into an even number of equal parts less than ten, and an odd number of those parts exist.

an even number less than 10 may be one of 2, 4, 6 or 8. so, the whole may be one of these four evens.

now, an odd number of these parts must exist, so the numerator must be an odd number, one of 1, 3, 5 or 7. it cannot be 9 because then the fraction will become improper.

thus, our fraction may be one of the following