If there is a 60% chance when you spin a penny tails come up...?

Question

IF spun 1000 times, What is the probability that the first two spins are tails? What about the 1000th one.

Answer 1

P(first 2 being tails) = 0.6*0.6 = 0.36

P(1000th one being a tail) =0.6

All of these spins are independent events. What happens in the first 999 does not affect the 1000th spin.

Answer 2

I've never heard that (a penny with a 60% chance of coming out tail) but let us assume that you have one.

The probability of any one spin coming out tail is 0.6 (= 60%); whether it is the first, seventh, two hundredth or 1000th spin, that is irrelevant.

In fact, even if you just got the first six to come out tail, the probability of the 7th spin to come out tail is still 0.6. Each spin is an 'independent event' which is not affected by the preceding events.

The probability of getting N tails when you spin the coin N times, is 0.6^N

First two spins? N=2
0.6^2 = 0.36 (36%)

1 spin = 0.6 (60%) probability of tail
2 spins= 0.36 (36%) probability of 2 tails
3 spins= 0.216 (21.6%) prob. of 3 tails
4 spins= 0.1296
5 spins= 0.07776
6 spins= 0.046656

At some point, if you are losing money on a bet and the penny was brought by the person taking you money, you should get suspicious...

However, the probability never gets to zero. it gets very small but it is always possible (just improbable)

1000 spins = 0.0000.... (there are 222 zeroes before the first significant digits) ...14166...

The probability (that ALL 1000 spins are tail) is not EXACTLY zero, but it is very close to zero.

Answer 3

The probability of any spin being tails is 60% = 6/10.

So when you spin one coin, there's a 6/10 chance of it being tails. Spin another coin, and there's a 6/10 chance of that one being tails too.

The probability of BOTH being tails is 6/10 * 6/10 = 36/100 or 36%.

The probability of the 1,000th coin alone being tails is still 6/10 = 60%. Or did you mean the probability of ALL 1,000 coins being tails? That would be
6/10 * 6/10 * ... * 6/10 <-- multiplied 1,000 times, or
(6/10)^1000 which is an incredibly small number.

Answer 4

Uh, I would say 50% chance.. But since you said you are spinning it, I will act "tipsy" and say yes there is a 60% chance the first two spins will be tails.

Answer 5

well you must have been board ha? well its always a 50% chance no matter what!