Question

A coin is biased to show 35% heads and 65% tails. The coin is tossed twice. What is the probability that the coin
turns up tails on both tosses?

Answer 1

kinda stuck:\

Answer 2

P(H)=0.35
P(T) = 0.65

In simple context we use intuitive method to solve it:

Sample Space {HH,HT,TH,TT}

Now, Probability of getting Head in one toss is 0.35, so getting head in 2 toss is:
0.35x0.35 = 0.1225.--- 12.25%

Hence, for two tail to show up:
0.65x0.65 = 0.4225 = 42.25%
________________________________Clarification____________________________________
This is just for extra clarification, however you dont have to do this step.
Just prove the answers; we calculate P(HT)=P(TH) = 2x0.2275= 0.455 = 45.5%.
Adding all the probabilities together gives:
HH+HT+TH+TT = 1, according to theory.

Now check our calculations. = 12.25% + 42.25% + 45.5% = 100%.
______________________________________________________________________________

Answer 3

i knew it was easeir than it looked

Answer 4

perhaps u can help with another if u dont mind

Answer 5

One way is to use binomial distribution, which can be used in experiment with only 2 possible outcomes, for example like tossing a coin.

P = nCr p^r (1-p)^n-r

We have our P(Tail) = 0.65 and other is 0.35
P(getting 2 tail) = 2C1 (0.65)^2(0.35)^0 // This is same as getting two tail in 2 toss is getting no 2 or one head.

Therefore, P(Tail) = 0.4225 = 42.25%.
Same as the above solution. Either one is correct due to the fact that it is discrete.

Hope it helps