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1. Homework Statement

1. Homework Statement

A bag contains two biased coins: coin A shows Heads with a probability of 0.6, and coin B shows Heads with a probability 0.25. A coin is chosen at random from the bag and tossed three times.

Find the probability that the three tosses of the coin show two Heads and one Tail in any order.

## Homework Equations

## The Attempt at a Solution

Probabilities:

[itex] H_{A}=0.6 [/itex] and [itex] T_{A}=0.4 [/itex]

[itex] H_{B}=0.25 [/itex] and [itex] T_{B}=0.75 [/itex]

Possibilities for 2 heads and one tail in any order:

[tex] 3\left ( H \right )^{2}\left ( T \right ) [/tex]

Is this correct so far?

My question is how to incorporate the probability of picking coin A or coin B into the problem?