Question

A fair coin is tossed 4 times in a row. If X is the number of heads counted, which table gives the probability distribution of X?

Answer 1

@rational

Answer 2

whats the probability for getting heads on all 4 coins ?

Answer 3

1/2?

Answer 4

how ?

Answer 5

may i know why do you think it is 1/2

Answer 6

its a 50/50 chance to land on head.

Answer 7

its a 50/50 chance to land head on one coin

Answer 8

but when you have four coins, the probability for landing heads on "ALL" four coins need not be 1/2 right

Answer 9

the probability is actually 1/2*1/2*1/2*1/2 = 1/16

Answer 10

so what like 1/4?

Answer 11

oh sorry. 4 coins. my bad

Answer 12

Yes, another question
whats the probability for getting NOT getting heads in any of the four coins ?

Answer 13

1/2 each so total would be another 1/16?

Answer 14

Yep!
so P(X=0) is 1/16
and P(X=4) is also 1/16

Answer 15

Now, whats the probability of getting exactly ONE head ?

Answer 16

P(X=1) = ?

Answer 17

I would think 1/2 but i know thats not it

Answer 18

one way to get exactly ONE head is :

H T T T

Answer 19

notice that there are 3 other ways to get exactly ONE head :

T H T T
T T H T
T T T H

Answer 20

so the probability for getting exactly ONE head is 4/16 = 1/4

Answer 21

see if that makes sense

Answer 22

Yes it does, I see what you mean now. okay.

Answer 23

look at the options

Answer 24

A?

Answer 25

Yes! our work so far matches perfectly with option A

Answer 26

Yes thats why I said A, the work matches A and not others