Coin flipping sequence probability with biased coins

[galatius]

Thank you in advance to anyone willing to help me answer the following question!

I have 5 coins. Each coin is biased differently as follows:

Coin A: probability of heads = .51; probability of tails = .49
Coin B: probability of heads = .52; probability of tails = .48
Coin C: probability of heads = .53; probability of tails = .47
Coin D: probability of heads = .54; probability of tails = .46
Coin E: probability of heads = .55; probability of tails = .45

Assume that these biases are inherent to the coins themselves and not influenced by any environmental variance.

If I flip each of these coins one at a time, what is the probability that at least 3 of them will turn up heads?

I am able to wrap my feeble mind around calculating sequence probabilities when the probability of the events making up the sequence are equal. So, for example, if I wanted to know what the odds were of flipping 5 unbiased coins and getting at least 3 heads, I would simply calculate the number of possible sequences involving 3 heads or more and then divide by the number of total possible sequences.

But what do I do when the probabilities of different sequence events are biased as described above?

Again, many thanks in advance!

 

[royhaas]

This is simply more calculation. For example, you must calculate the probability that A, B, C are heads and D, E are tails by multiplying the probabilities together.

 

[galatius]

Thanks for the quick response.

If I understand you correctly, what I would need to do is identify every possible sequence and then calculate the unique probability for each sequence. So, for example, the probability of coins A, B, and C coming up heads while coins D and E come up tails would be:

.51 X .52 X .52 X .46 X .45 = .029

Is that correct?

What would I do once I have done that for every possible sequence? Would I then add together the sequence probabilities for all the sequences where at least 3 coins come up heads?

 

[royhaas]

You are correct. Add the probabilities for each sequence with three or more heads.