5 a A coin is tossed five times Determine the number of poss

5. a) A coin is tossed five times. Determine the number of possible outcomes for the five coin tosses where order matters, e.g., H-H-H-H-T and H-H-H-T-H count as two different outcomes (H=heads, T=tails). b) For the five coin tosses in part a) above, determine: i) P(all five heads) ii) P(at least one tails)

Solution

a) Number of possible outcome for toss of one coin = 2 {H,T}

Number of possible outcome for toss of two coins = 2² = 4 {H-H,H-T,T-H,T-T}

Therefore, Number of possible outcome for toss of five coins = 2⁵ = 32

b)

i) There is only one event with all five heads, (H-H-H-H-H).

Therefore, P(all five heads) = 1/32

ii) There is only one event with no tails, (H-H-H-H-H). Rest all events has atleast one tails.

Therefore, P(at least one tails) = 1 - P(all five heads) = 1 - 1/32 = 31/32