SOLUTION: Please! help me understand mean ,exactly,atmost,neither, thank you so much Find probability if a coin is tossed 5 time P(0 tails) P(exactly 1 tail) P(at most 2 tails) P(at lea

Question 394210: Please! help me understand mean ,exactly,atmost,neither, thank you so much
Find probability if a coin is tossed 5 time
P(0 tails)
P(exactly 1 tail)
P(at most 2 tails)
P(at least 4 tails)
Found 2 solutions by stanbon, josmiceli:
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
Find probability if a coin is tossed 5 time
P(0 tails) = P(5 heads) = (1/2)^5 = 1/32
--------------------------
P(exactly 1 tail) = 5C1(1/2)(1/2)^4 = 5(1/32) = 5/32
--------------------------
P(at most 2 tails) = P(0,or 1, or 2 tails) = (1/32) + (5/32) + 5C2(1/2)^5
= 6/32 + 10/32 = 16/32 = 1/2
-----------------------------------
P(at least 4 tails) = P(4 or 5 tails) = 5C4(1/2)^5 + 5C5(1/2)^5
= 5/32 + 1/32 = 6/32 = 3/16
==============================
Cheers,
Stan H.
============
Answer by josmiceli(19441) (Show Source): You can put this solution on YOUR website!
It is equally likely that a fair coin will come up H or T
In probabilities we say
P(H) = 1/2
P(T) = 1/2
Note that P(H) + P(T) must add up to 1, since 1 = certainty, and
it is certain that nothing else can happen (no losing coin allowed)
----------------------------
P(0 tails) = P(5 heads) for 5 tosses
What you're doing is tossing the coin and saying I want Heads 5 time
in a row, or H and H and H and H and H. When ever you want to find
P(A and B and C...) you must MULTIPLY the separate probabilities, so
1st toss P(H) = 1/2
2nd toss P(H) = 1/2
3rd toss P(H) = 1/2
4th toss P(H) = 1/2
5th toss P(H) = 1/2
P(5 heads) = (1/2)^5
(1/2)^5 = 1/32 answer
--------------------
Exactly 1 tail means you only want to see
either:
THHHH
HTHHH
HHTHH
HHHTH
HHHHT
In the previous problem, I found there are 32 possible outcomes
for 5 tosses , 1 of which was HHHHH. Now I want only 1 of the
above 5 choices.
So, P(exactly 1 T) = 5/32
Note that you add the P of each because you want P (THHHH OR HTHHH OR ... etc.)
and generally P(A or B) = P(A) + P(B)
----------------------
At most 2 tails
This means 1 tail is OK OR 2 tails is OK , but all others are rejected
I want to find P(1 tail) + P(2 tails)
1 tail would be
THHHH or
HTHHH or
HHTHH or
HHHTH or
HHHHT
So, P(1 tail) = 5/32
What are all the possible ways you can get exactly 2 tails and 3 heads?
That is the permutation of 5 things taken 2 at a time.
You can look that up. I'm out of time, sorry

RELATED QUESTIONS
An unfair coin has probability p of landing heads up on a single flip, where 0 < p < 1.... (answered by greenestamps)
Probabilities in Coin Tossing: Three fair coins are tossed. (a) Write out the... (answered by ewatrrr)
Please help me understand ... If represents a random variable coming from a normal... (answered by Theo)
Please! HELP me with my sonhome work A die rolled 3 time. Find probability P(1 then 2... (answered by ewatrrr)
Suppose a fair coin is tossed twice. Find the probability for each of the following:... (answered by drk)
This problem is really frustrating me, I just don't understand, will someone please help? (answered by stanbon)
Can someone help me with this problem? Its urgent and I dont understand it!! A... (answered by Natolino1983,robertb)
a bag contains 2 red, 4 yellow, and 6 blue marbles. two marbles are drawn without... (answered by stanbon)
5. A random experiment consists of tossing three fair coins and recording whether each... (answered by Boreal)