a coin is tossed 5 times . find P(at most 4 tails).?

Question

a. 3/16
b. 13/16
c. 1/32
d. 31/32

Answer 1

P (five tails) = 1/32, so the answer is d.

Answer 2

The answer is d. Use the rule of complements:

P(at most 4 tails) = 1 - P(5 tails) = 1 - 1/2^5 = 32/32 - 1/32 = 31/32

Answer 3

P(at most 4 tails) =
1 - P(5 tails) =
1 - (1/2)^5 =
31/32

Answer 4

choice d. 31/32

you cannot have have 5 tails. probability of 5 tails =
1/2 * 1/2 * 1/2 * 1/2 * 1/2 = 1/32

therefor probability of at most 4 tails = 1 - 1/32 = 31/32

Answer 5

P(at most 4 tails) = P(0 tails) + P(1 tail) + P(2 tails) + P(3 tails) + P(4 tails)
this follows a binomial distribution with probability of success(tail shows) .5

so you have

P(T = 0) = 1(.5)^0 *(.5)^5
P(T = 1) = 5_C_1 (.5^1) (.5^4)
...

p(t <=4) = .5^5(1 + 5 + 10 + 10 + 5)
= 1/32(31) = 31/32