# Math Help - probability help

1. ## probability help

A fairground game involves trying to hit a moving target with a gunshot. A round consists of up
to 3 shots. Ten points are scored if a player hits the target, but the round is over if the player
misses. Linda has a constant probability of 0.6 of hitting the target and shots are independent of

one another.

(a) Find the probability that Linda scores 30 points in a round.

$0.6^3 = 0.216$

The random variable X is the number of points Linda scores in a round.

(b) Find the probability distribution of X.
x = 0, 10 , 20 , 30
p(x) 0.4 0.24 0.144 0.216
(c) Find the mean and the standard deviation of X.
$E(X) = 11.76$

$SD = 11.7$

A game consists of 2 rounds.
(d) Find the probability that Linda scores more points in round 2 than in round 1.

I need help woth the last question, 'd', How do I start?

2. Originally Posted by Tweety

(a) Find the probability that Linda scores 30 points in a round.

$0.6^3 = 0.216$

The random variable X is the number of points Linda scores in a round.

(b) Find the probability distribution of X.
x = 0, 10 , 20 , 30
p(x) 0.4 0.24 0.144 0.216
(c) Find the mean and the standard deviation of X.
$E(X) = 11.76$

$SD = 11.7$

A game consists of 2 rounds.
(d) Find the probability that Linda scores more points in round 2 than in round 1.

I need help woth the last question, 'd', How do I start?

Hi Tweety,

For (d), use your results from (b).

Let's say the result of the first round is X and the result of the second round is Y. There are only 4 possibilities for each, so you should find it easy to list all the pairs (x,y) where x < y. Use independence of X and Y, along with your results from (b), to find the probability of each (x,y) pair. Then add the probabilities up.