Sarah estimates that there is a 40% chance that she will belate for class if she

Question

Sarah estimates that there is a 40% chance that she will belate for class if she misses the 8:30 bus/ There is a 20% chaancethat she will miss the 8:30 bus on any given day. a.) what is the probability trhat she will miss hwer bustommorrrow but still be on time b.) if there is a 10% chance that Sarah will be late, even uifshe catches the 8:30 bus, qwhat is the probabilkity that she willbe late on any gtiven day? Sarah estimates that there is a 40% chance that she will belate for class if she misses the 8:30 bus/ There is a 20% chaancethat she will miss the 8:30 bus on any given day. a.) what is the probability trhat she will miss hwer bustommorrrow but still be on time b.) if there is a 10% chance that Sarah will be late, even uifshe catches the 8:30 bus, qwhat is the probabilkity that she willbe late on any gtiven day?

Explanation / Answer

a.) the probability that she will miss her bus tomorrow butstill be on time = P(M and L') = P(L'/M) x P(M)
= 0.6 x 0.2 = 0.12

b.) if there is a 10% chance that Sarah will be late, even ifshe catches the 8:30 bus,
i.e, P(L / M') = 0.1
probability that sarah will be in time if she catches the bus =P(L'/M') = 1-0.1 = 0.9

the probability that she will be late on any given day = {P(L/M') xP(M') }+{P(L / M)x P(M) }
= (0.1 x 0.8 ) + (0.4 x 0.2)
= 0.08 +0.08 =0.16

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