s1 help, Discrete random variables.

A game is made in which you have to hit a moving target, with an air rifle.
a player has up to 3 pellets in a round. 5 points are scored if a target is hit, but the round is over if missed.

J has a constant probability of 0.4 of hitting the target.

X is the random variable, no. of point scored in a round.

a.find the probability that J gets 15 points in a round. I got 0.064
b.find the probability distribution of x. when x=0. i got 0.6
x=5, 0.24
x=10, 0.096
x= 15, 0.064
A game consists of 2 rounds.

c. find the probability that J scores more on the 2 round that the first.

I have no idea on how to answer c, any help is appreciated. Thanks

Here is a start

Scores 5 in first round and then more in the next round = 0.24 x (0.096+0.064)

Does that help

I see that in the first round, if you only score 5 points, that a probability of 0.24, but I don't see why you multiplied by (0.096+0.064)

Because you want him to score more than 5 in the second round

so to get more that 5, you add the probabilities of 10 and 15, as they are higher and so the probabilities are (0.096+0.064), the you times them.

Ok, what should i do next?

Consider the other options (other than 5 in the first round)

could score 10 in first round, then 15 in next so, 0.096 x 0.064, right?

and those are the only options left?

Is there nothing else that you can score in round one?

Oh yeah, the 0, so its 0.6 X (0.096 + 0.064 + 0.24)

indeed

What shall I do next?

seriously?

you have some viable options, what would you usually do with the probabilities to get the total probability

Add, them?

yes

I see, 1 more q, why do you add them?

Why wouldn't you

This is GCSE maths
P(A and B) = P(A) x P(B)
P(A or B) = P(A) + P(B) (if mutually exclusive)

I see, makes sense. Thanks