Question

A video game gives a special bonus when the player collects a coin if the player collects the coin at the
moment when the last digit of the milliseconds in the game's timer equals 1. Players don't see this timer, so
all 10 digits are equally likely, and there is a 1 in 10 chance that a player gets the bonus on any given coin
collected. Let C be the number of coins a player has to collect to first get the bonus. Assume that the last
digits are independent of each other.

Answer 1

Answer:

.07

Step-by-step explanation:

khan answer

Answer 2

Probabilities are used to determine the chances of events.

The probability that the player gets the bonus on the 4th coin is 0.0729

The probability (p) of getting a bonus is given as:

$p = \frac 1{10}$

The probability (q) of not getting a bonus is calculated using the complement rule:

$q = 1 - p$

So, we have:

$q = 1 - \frac{1}{10}$

Take LCM

$q =\frac{10 - 1}{10}$

$q =\frac{9}{10}$

The event that the player gets the bonus on the 4th coin is represented as:

Event = qqqp

So, the probability is:

$Pr = q^3p$

Substitute values for q and p

$Pr = (9/10)^3 \times (1/10)$

Express as decimals

$Pr = (0.90)^3 \times 0.10$

Multiply

$Pr = 0.0729$

Hence, the probability that the player gets the bonus on the 4th coin is 0.0729

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