What is the probability that with three flips of a coin all three flips will be the same?

Solution:

Let's look into all the possible outcomes on three flips of a coin.

Probability of an event (E) = Number of favorable outcomes / Total number of outcomes

Let H = Heads, T = Tails

When 3 coins are tossed,

Sample space S = {HHH, HHT, HTH, HTT, THH, THT, TTH, TTT}

Total number of outcomes n(S) = 8

Number of outcomes that gives the same results in all the three flips of a coin P(all 3 flips same) = 2

n(A) = {HHH, TTT}

n(A) = 2

P(all three flips will be the same) = Number of favorable outcomes / Total number of outcomes

= n(A)/n(S)

= 2/8

= 1/4

Therefore, the probability that with three flips of a coin all three flips will be the same is 1/4.

What is the probability that with three flips of a coin all three flips will be the same?

Summary: 

The probability that with three flips of a coin all three flips will be the same is 1/4.