Question

Hi, I have got this question for a quiz, please help me solving it.

1. A coin is tossed 5 times.
a. In how many ways do at least 4 head occur?
b. Show your answer in terms of sets and prove it using C (n, r).

Note: I have answerd part (a) see the posted file and tell me if it is wrong, I don't know how to do part (b)???

Answer 1

Here is the file for part (a)

Answer 2

your document doesn't seem to answer the question in your post, which is how many ways 4 heads can occur, not the probabilty

Answer 3

at least 4 heads*

Answer 4

do you mean my answer is partly correct, and the missing is that I have to mention this (at least 4 heads)?

Answer 5

you calculated the correct probability of getting at least 4 heads, but the question is asking for the *total number of ways" you can get at least 4 heads, which is implicit in your answer

Answer 6

ok good, then what about part (b)?

Answer 7

I'm not sure what they mean by "show in terms of sets" but my answer would be along the lines of
"the number of ways to get at least k heads out of n trials is the same as the number of ways to select at least k elements from n elements, which is\[\large\sum_{i=k}^n\binom nk\]

Answer 8

Well, since I don't have enough time, I'll post your answer for part (b), hoping it is correct. Thank you for your help. ^_^