A coin is tossed 5 times. Find the probability that all are heads. Find the probability that at most 2 are heads.

Answer:1/3215/32Step-by-step explanation:For a fair sided coin, Probability of heads, P(H) = 1/2Probability of tails P(T)  = 1/2For 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 1/32hence 15 outcomes for "at most 2 heads" have a probability of (1/32) x 15  = 15/32