Question

If we toss a coin 4 times, what are the number of outcomes? Is it equal tossing 4 coins simultaneously? i.e. no. of outcomes=2⁴=16

And what if we toss a pair of coins two times? Is it also equal to tossing 4 coins simultaneously? i.e. no. of outcomes is 16?

Answer 1

(1)

The event of tossing a coin 4 times will yield the following outcomes,

{H, T} on first toss

Similarly, {H, T} on second toss.

So, all possible outcomes when we toss a coin 4 times are {H, T, H, T, H, T, H, T} = 8

The event of tossing 4 coins simultaneously will yield 2⁴ = 16 outcomes.

{(HHHH), (HHHT), (HHTT), ... so on}

So, both these events will yield different number of outcomes.

(2)

Now, if we toss a pair of coins two times, we get the following outcomes:

{HH, HT, TH, TT} on first toss

{HH, HT, TH, TT} on second toss.

So, all possible outcomes when we toss a pair of coins twice are {HH, HT, TH, TT, HH, HT, TH, TT} = 8

This is not equal to tossing 4 coins simultaneously as we get 16 outcomes as explained in the previous part.