Anna travels to work by car or by bicycle .

The probability that she travels by car is 0.35 .
If she travels to work by car ,the probability that she will be late is 0.12 .If she travels to work by bicycle,the probability that she will late is 0.25..Work out the probability that she will not be late.

I think it is 0.66 ..

prob late = .35*.12 +(1-.35)*.25

= .205

1 - .205 = .8

Thank you very much for your help. Is any chance that you can help me with other questions which I posted already,please

To find the probability that Anna will not be late, we need to consider two scenarios: when she travels by car and when she travels by bicycle.

Scenario 1: Anna travels by car
The probability that Anna travels by car is given as 0.35. The probability that she will be late given that she travels by car is 0.12. Therefore, the probability that she will not be late when she travels by car is 1 - 0.12 = 0.88.

Scenario 2: Anna travels by bicycle
The probability that Anna travels by bicycle is 1 - 0.35 = 0.65 (since traveling by car and bicycle are the only options). The probability that she will be late given that she travels by bicycle is 0.25. Thus, the probability that she will not be late when she travels by bicycle is 1 - 0.25 = 0.75.

To calculate the overall probability that Anna will not be late, we need to consider both scenarios using the law of total probability:

P(Not Late) = P(Not Late|Car) * P(Car) + P(Not Late|Bicycle) * P(Bicycle)

P(Not Late) = (0.88 * 0.35) + (0.75 * 0.65) = 0.308 + 0.4875 = 0.7955

Therefore, the probability that Anna will not be late is approximately 0.7955 or 79.55%.