Question

Let X = the number of heads in 4 flips of a fair coin. Use the probability distribution of X found here to calculate the

probability of each event.
at least 2 heads
exactly 2 heads
not all heads
more than 2 heads
0.3125
0.9375
0.6875
0.375

Answer 1

You could answer using a Binomial Distribution but let’s try the sample space

There are a total of 16 possible outcomes
No heads TTTT
One head HTTT, THTT, TTHT, TTTH
Two heads HHTT, HTHT, HTTH, THHT, THTH, TTHH
Three heads HHHT, HHTH, HTHH, THHH
Four heads HHHH
Because P(H) = P(T) they are all equally likely (it is a fair coin)

P(at least 2 heads) = 11/16 = 0.6875
P(exactly 2 heads) = 6/16 = 3/8 = 0.375
P(not all heads) = 1 - P(all heads) = 15/16 = 0.9375
P(more than 2 heads) = 5/16 = 0.3125