Answer:
1/32
15/32
Step-by-step explanation:
For a fair sided coin,
Probability of heads, P(H) = 1/2
Probability of tails P(T) = 1/2
For a coin tossed 5 times,
P( All heads)
= P(HHHHH),
= P (H) x P(H) x P(H) x P(H) x P(H)
= (1/2) x (1/2) x (1/2) x (1/2) x (1/2)
= 1/32 (Ans)
For part B, it is easier to just list the possible outcomes for
"at most 2 heads" aka "could be 1 head" or "could be 2 heads"
"One Head" Outcomes:
P(HTTTT), P(THTTT) P(TTHTT), P(TTTHT), P(TTTTH)
"2 Heads" Outcomes:
P(HHTTT), P(HTHTT), P(HTTHT), P(HTTTH), P(THHTT), P(THTHT), P(THTTH), P(TTHHT), P(TTHTH), P(TTTHH)
If we count all the possible outcomes, we get 15 possible outcomes representing "at most 2 heads)
we know that each outcome has a probability of 1/32
hence 15 outcomes for "at most 2 heads" have a probability of
(1/32) x 15 = 15/32
