Mistake in probabilities
P(XP) is supposed to be 0.45, but you have used 0.4 instead while applying Baye's rule.
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The second number in the numerator is indeed mistaken and should instead be 0.45. The lecturer does say '0.45' and the final answer - 0.375 - is obtained when using the number 0.45 in the calculation, so I hope this mistake hasn't caused a lot of confusion.