examday

/TMUA

Box $A$ contains $2$ red counters and $3$ blue counters. Box $B$ contains $3$ red counters and $1$ blue counter.

A fair coin is tossed. If it lands heads, a counter is taken at random from box $A$; if tails, a counter is taken at random from box $B$.

The counter taken is red. Find the probability that it came from box $B$.