Question

A coin is weighted so that there is a 68% chance that it will come up "heads" when flipped. The coin is flipped four times. Find the probability of getting exactly three heads. Round your answer to four decimal places.

Answer 1

Since the coin is weighted means that the probability of getting Heads is higher.

P(Heads)= 0.68

SInce there are only 2 possible outcomes and probability must be 1 then the probability of getting tails will be:

P(tails)= 1-0.68

P(tails)=0.32

Remember that to find the probability of events that occur one after another we should multiply the probability for each one of them

THREE HEADS AND 1 TAILS

we should find what are the possible outcomes.

HHHT, HTHH, HHTH, THHH

then multiply the probabilities for each of the possible outcomes.

P(HHHT)= (0.68)*(0.68)*(0.68)*(0.32)

p(HHHT)= 0.1006

Although they are different outcomes, the probability for each one them is the same.

the probability of 3 heands and 1 tail is adding all the possible ones.

3h1t: 3 heads 1 tail

P(3h1t)=0.1006+0.1006+0.1006+0.1006

P(3h1t)= 0.4024

Answer: the probability of getting exactly 3 heads will be 0.4024