## Trying Until You Succed

You might pass at the first attempt. The probability of this is 0.7.

You might fail the first attempt and retake, passing at the second attempt. The probability of failing the first attempt and passing at the second attempt is 0.3 x 0.7=0.21.

You might fail the first attempt, fail the second attempt and pass at the third attempt. The probability of this is 0.3 x 0.3 x 0.7=0.063.

The verall probability of passing within three attempts is

0.7+0.3 x 0.7 + 0.3 x 0.3 x 0.7=0.973.