Question

Miss $X$ takes either tea or coffee at morning break. If she had tea one morning, the probability that she has tea the next morning is $\mathrm{0.4.}$ If she had coffee one morning, the probability that she has coffee the next morning is $\mathrm{0.3.}$ Suppose she has coffee on a Monday morning. The probability that she has tea on the following Wednesday morning, is

• A. $0.46$
• B. $0.49$
• C. $0.51$
• D. $0.61$

Answer 1

The correct option is B $0.49$

Let $C$ be the event that she had tea
and $T$ be the probability that she had coffee.

Let $E$ be the event that she has tea on the following Wednesday morning given she has coffee on a Monday morning.
Then, $P\left(E\right)=P\left(CCT\right)+P\left(CTT\right)$
$=\left(0.3\right)\left(0.7\right)+\left(0.7\right)\left(0.4\right)=0.21+0.28=0.49$