Question

(04.06 mc)
the chance of winning based on the type of lottery tickets we purchase is 0.05, or 1 in 20. we know to stop after we win, so this will be a geometric setting. we will play each saturday until we win. what is the probability of winning on the second ticket?

0.05

0.0451

0.0475

0.0429

Explanation:

Step1: Define success/failure probabilities

Let $p = 0.05$ (win probability), so $1-p = 1-0.05 = 0.95$ (lose probability).

Step2: Apply geometric distribution formula

To win on the 2nd ticket, lose 1st, win 2nd: $P(X=2) = (1-p)^{1} \times p$
<Expression>
$P(X=2) = 0.95 \times 0.05$
</Expression>

Step3: Calculate the result

<Expression>
$P(X=2) = 0.0475$
</Expression>

Answer:

0.0475